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THE    GREAT    TELESCOPE    OF    THE    UNITED    STATES     NAVAL    OBSERVA= 
TORY,   WASHINGTON. 

COKSTBUCTED   BY    ALTAX    CLARK    AND   SONS,  1873. 


POPULAR  ASTRONOMY. 


BY 


SIMON    NEWCOMB,   LL.D., 

SUPERINTENDENT  AMERICAN  NAUTICAL  ALMANAC, 
FORMERLY  PROFESSOR  AT  TUE  U.  8.  NAVAL  OUSERVATOEY. 


WITH  ONE  HUNDRED  AND   TWELVE  ENGRAVINGS, 
AND  FIVE  MAPS  OF  THE  STARS. 


SIXTH   EDITION  REVISED. 


NEW    YORK: 

HARPER    &    BROTHERS,    PUBLISHERS, 

FRANKLIN    SQUARE. 

189  2. 


Entered  according  to  Act  of  Congress,  in  the  year  1882,  by 

Harper    &    Brothers, 

in  the  OflSce  of  the  Librarian  of  Congress,  at  Washington, 


/  Y  V  ->-  otiences 

,   -■  T  '  Libraiy 


PREFACE. 


To  prevent  a  possible  misapprehension  in  scientific  quar- 
ters,  the  author  desires  it  understood  that  the  present  work 
is  not  designed  either  to  instruct  the  professional  investi- 
gator or  to  train  the  special  student  of  astronomy.  Its  main 
object  is  to  j^resent  the  general  reading  public  with  a  con- 
densed view  of  the  history,  methods,  and  results  of  astro- 
nomical research,  especially  in  those  fields  which  are  of  most 
popular  and  philosophic  interest  at  the  jDresent  day,  couched 
in  such  language  as  to  be  intelligible  without  mathematical 
study.  He  hopes  that  the  earlier  chapters  will,  for  the  most 
part,  be  readily  understood  by  any  one  having  clear  geomet- 
rical ideas,  and  that  the  later  ones  will  be  intelligible  to  all. 
To  diminish  the  difficulty  which  the  reader  may  encounter 
from  the  unavoidable  occasional  use  of  technical  terms,  a 
Glossary  has  been  added,  including,  it  is  believed,  all  that 
are  used  in  the  present  work,  as  well  as  a  number  of  others 
which  may  be  met  with  elsewhere. 

Respecting  the  general  scope  of  the  work,  it  may  be  said 
that  the  historic  and  philosophic  sides  of  the  subject  have 
been  treated  with  greater  fulness  than  is  usual  in  works  of 
this  character,  while  the  purely  technical  side  has  been  pro- 
portionately condensed.  Of  the  four  parts  into  Avhich  it  ia 
divided,  the  first  two  treat  of  the  methods  by  which  the  mo- 


% 


vi  PREFACE. 

tions  and  the  mutual  relations  of  the  heavenly  bodies  have 
been  investigated,  and  of  tlie  results  of  such  investigation, 
while  in  the  last  two  the  individual  peculiarities  of  those 
bodies  are  considered  in  greater  detail.  The  subject  of  the 
general  structure  and  probable  development  of  the  universe, 
which,  in  strictness,  might  be  considered  as  belonging  to  the 
first  part,  is,  of  necessity,  treated  last  of  all,  because  it  re- 
quires all  the  light  that  can  be  thrown  upon  it  from  every 
available  source.  Matter  admitting  of  presentation  in  tabular 
form  has,  for  the  most  part,  been  collected  in  the  Appendix, 
where  will  be  found  a  number  of  brief  articles  for  the  use 
of  both  the  general  reader  and  the  amateur  astronomer. 

The  author  has  to  acknowledge  the  honor  done  him  by 
several  eminent  astronomers  in  making  his  work  more  com- 
plete and  interesting  by  their  contributions.  Owing  to  the 
great  interest  which  now  attaches  to  the  question  of  the  con- 
stitution of  the  sun,  and  the  rapidity  with  which  our  knowl- 
edge in  tliis  direction  is  advancing,  it  was  deemed  desirable 
to  present  the  latest  views  of  the  most  distinguished  investi- 
gators of  this  subject  from  their  own  pens.  Four  of  these 
gentlemen— Kev.  Father  Secchi,  of  Kome ;  M.  Faye,  of  Paris ; 
Professor  Young,  of  Dartmouth  College ;  and  Professor  Lang- 
ley,  of  Allegheny  Observatory — have,  at  the  author's  request, 
presented  brief  expositions  of  their  theories,  which  will  be 
found  in  their  own  language  in  the  chapter  on  the  sun. 


PREFACE 

TO  THE   SEVENTH  EDITION. 


The  favor  with  which  this  work  has  been  received  by  the 
pnl)lic  has  led  the  author  and  publishers  to  give  it  a  sixth  re- 
vision, in  order  to  inckide  the  latest  results  of  astronomical 
research.  The  subjects  which  were  added  in  preceding  edi- 
tions comprised  Dr.  Draper's  investigations  on  the  existence 
of  oxygen  in  the  sun  ;  Janssen's  new  method  of  photographing 
the  sun;  the  conclusions  from  recent  total  eclipses;  the  pre- 
liminary results  of  the  British  observations  of  the  late  transit 
of  Venus,  as  well  as  of  other  methods  of  determining  the 
solar  parallax;  the  discovery  of  the  satellites  of  Mars;  t|ie 
transit  of  Venus  of  December  6th,  18S2  ;  recent  developments 
in  cometary  astronomy ;  Professor  Langley's  researches  on 
the  light  and  heat  radiated  by  the  sun  ;  and  the  completion 
of  several  of  the  greatest  telescopes  ever  made,  including  that 
of  the  Lick  observatory  in  California.  The  subject  of  greatest 
interest  now  included  for  the  first  time  is  the  determination  of 
the  motion  of  certain  stars  by  Vogel,  Pickering,  and  Chandler. 
The  intention  has  been  to  bring  the  work  up  to  date  in  all 
important  points,  and  it  is  hoped  that  the  general  reader  will 
find  in  it  the  fullest  practicable  explanation  of  every  branch 
of  the  subject  which  can  interest  him. 

Washington,  March,  1893. 


CONTENTS. 


PART  I. 

THE  SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

PAGK 

Introduction 1 


CHAPTER  I. 

The  Ancient  Astronomy,  or  the  Apparent  Motions  of  the  Heav- 
enly Bodies 7 

§1.  The  Celestial  Sphere 7 

§2.  The  Diurnal  Motion 9 

§3.  Motion  of  the  Sun  among  the  Stars 13 

§  4.  Precession  of  the  Equinoxes. — The  Solar  Year 19 

§5.  The  Moon's  Motion 2i 

§6.  Eclipses  of  the  Sun  and  Moon 24 

§7.  Tlie  Ptolemaic  System 32 

§8.  The  Calendar 44 


CHAPTER  11. 

The  Copernican  System,  or  the  True  Motions  of  the  Heavenly 

Bodies 51 

§  1.  Copernicus 51 

§  2.  Obliquity  of  the  Ecliptic  ;  Seasons,  etc. ;  on  the  Copeniicaii  Sys- 
tem   Gl 

§3.  Tycho  Brahe 66 

§4.  Kepler. — His  Laws  of  Planetary  Motion 68 

I  §5.  From  Kepler  to  Newton 71 


X  COXTEXTS. 

CHAPTER  III.  PAOB 

Universal  Gravitation 74 

§1.  Newton. — Discovery  of  Gravitation 74 

§  2.  Gravitation  of  Small  Masses. — Density  of  the  Earth 81 

§3.  Figure  of  the  Earth 86 

§4.  Precession  of  the  Equinoxes 88 

§5.  The  Tides 90 

§  C.  InequaUties  in  the  Motions  of  the  Phanets  produced  by  their 

Mutual  Attraction Uiy 

§  7.  Relation  of  the  Planets  to  the  Stars i03 


PAET  II. 

PEACTICAL  ASTBOXOMY. 
Introductory  Remarks 105 

Cn.\PTER  I. 

The  Telescope 108 

§  1.  The  First  Telescopes 108 

§2.  The  Achromatic  Telescope 116 

§3.  The  Mounting  of  the  Telescope 120 

§4.  The  Reflecting  Telescope 123 

§  5.  The  Principal  Great  Reflecting  Telescopes  of  Modem  Times...  127 

§6.  Great  Refracting  Telescopes 137 

§  7.  The  Magnifying  Powers  of  the  Two  Classes  of  Telescopes 141 

CHAPTER   II. 

Application  of  the  Telescope  to  Celestial  Measurements 148 

§  1.  Circles  of  the  Celestial  Sphere,  and  their  Relations  to  Positions 

on  the  Earth 148 

§2.  The  Meridian  Circle,  and  its  Use 154 

§3.  Determination  of  Terrestrial  Longitudes 159 

§  4.  Mean,  or  Clock,  Time 164 


CONTENTS.  Xi 

CHAPTER  III.  P^OE 

Measuring  Distances  in  the  Heavens 167 

§1.  Parallax  in  General 167 

§  2.  Measures  of  the  Distance  of  the  Sun 173 

§3.  Solar  Parallax  from  Transits  of  Venus 177 

§  4.  Other  Methods  of  Determining  the  Sun's  Distance,  and  their 

Results 192 

§  o.  Stellar  Parallax 199 

CHAPTER  IV. 
The  Motion  of  Light 208 

CHAPTER  V. 
The  Spectroscope 220 


PART  III. 

THE  SOLAR  SYSTEM. 


CHAPTER  I. 
General  Structure  of  the  Solar  System 231 


CHAPTER  II. 

The  Sun 237 

§  1.  The  Photosphere  and  Solar  Radiation 237 

§2.  The  Solar  Spots  and  Rotation 248 

§3.  Periodicity  of  the  Spots 254 

§4.  Law  of  Rotation  of  the  Sun 255 

§5.  The  Sun's  Surroundings 257 

§6.  Physical  Constitution  of  the  Sun 264 

§  7.  Views  of  Distinguished  Students  of  the  Sun  on  the  Subject  of 

its  Physical  Constitution 271 


Xll  CONTENTS. 

CHAPTER  III.  ,A8E 

The  IsnsEU  Grottp  of  Placets. 289 

§1.  The  Planet  Mercury 289 

§2.  The  Supposed  Intra-Mercurial  Planets 292 

§3.  The  Planet  Venus 295 

§4.  The  Earth 304 

§5.  The  Moon 312 

§6.  The  Planet  Mars 326 

§7.  The  Small  Planets 331 

CHAPTER  IV. 

The  Octer  Group  of  Plaxets 339 

§  1.  The  Planet  Jupiter 339 

§2.  The  Satellites  of  Jupiter 34-t 

§  3.  Satuiti  and  its  System,  Physical  Aspect,  Belts,  Rotation 346 

§4.  The  Rings  of  Satura 34H 

§5.  Constitution  of  the  Ring 357 

§6.  The  Satellites  of  Satuni 359 

§7.  Uranns  and  its  Satellites 361 

§8.  Neptune  and  its  Satellite 366 

CHAPTER  V. 

Comets  asd  Meteors 373 

§1.  Aspects  and  Forms  of  Comets 373 

§  2.  Motions,  Origin,  and  Number  of  Comets 377 

§3.  Remarkable  Comets 382 

§4.  Encke's  Comet,  and  the  Resisting  Medium 393 

§5.  Other  Periodic  Comets 396 

§6.  Meteors  and  Shooting-stars 397 

§7.  Relations  of  Comets  and  Meteoroids 404 

§8.  The  Physical  Constitution  of  Comets 411 

§9.  The  Zodiacal  Light 416 


PART  IV. 

THE  STELLAR  UNIVERSE. 

Introdcctory  Remarks 418 


CONTENTS.  Xiii 

CHAPTER  I.  p^„ 

The  Stars  as  they  ark  Seen 422 

§  1.  Number  and  Orders  of  Stars  and  Nebula; 422 

§2.  Description  of  the  Principal  Constellations 429 

§3.  New  and  Variable  Stars 433 

§4.  Double  Stars 448 

§5.  Clusters  of  Stars 453 

§  6.  Nebulae 450 

§7.  Proper  Motions  of  the  Stars 4G4 


CHAPTER  II. 

The  Sfructure  of  the  Universe 472 

§1.  Views  of  Astronomers  before  Ilerschel 473 

§  2.  Researches  of  Herschel  and  his  Successors 477 

§3.  Probable  Arrangement  of  the  Visible  Universe 490 

§4.  Do  the  Stars  really  form  a  System? 495 


CHAPTER   III. 

The  Cosmogony 503 

§  1.  The  Modern  Nebular  Hypothesis 505 

§2.  Progressive  Changes  in  our  System 511 

§3.  The  Sources  of  the  Sun's  Heat 517 

§4.  Secular  Cooling  of  the  Earth 523 

§5.  General  Conclusions  respecting  the  Nebular  Hypothesis 526 

§6.  The  Plurality  of  Worlds 528 


APPENDIX. 

I.  List  of  the  Principal  Great  Telescopes  of  the  World 533 

II.  List  of  the  more  Remarkable  Double  Stars 534 

III.  List  of  the  more  Interesting  and  Remarkable  NEBtJL.a!:  and 

Star  Clusters 537 

IV.  Periodic  Comets  seen  at  more  than  One  Return 539 


xiv  coNTi::sTs. 

TAGt 

V.  Elements  of  tke  Orbits  of  the  Eight  Major  Planets  for  18.")0.  540 

Elements  of  the  Satellites  of  Jdpitee 541 

Elements  of  the  Satellites  of  Saturn 541 

Elements  of  the  Satellites  of  Mars 541 

Elements  of  the  Satellites  of  Uranus 541 

Elements  of  the  Satellite  of  Neptune 541 

VI.  Elements  of  the  Small  Planets 542 

VII.  Determinations  of  Stellar  Parallax 548 

VIII.  Synopsis  of  Papers  on  the  Solar  Parallax,  1854-77 551 

IX.  List  of  Astronomical  Works,  most  of  which  have  been  con- 
sulted as  Authorities  in  the  Preparation  of  the  Present 

Work 555 

X.  Glossary  of  Technical  Terms  of  Frequent  Occurrence  in 

Astronomical  Works 562 

Index , 573 

Explanation  of  the  Star  Maps ».  578 


LIST  OF  ILLUSTRATIONS. 


FI«».  PAQR 

Thk  Great  Telescope  of  the  United  States  Naval  Observato- 
ry, Washington Frontispiece 

1.  Section  of  the  Imaginary  Celestial  Sphere 3 

2.  Map  illustrating  the  Diurnal  Motion  round  the  Pole 10 

3.  The  Celestial  Sphere  and  Diurnal  Motion 1'-' 

4.  Motion  op  the  Sun  past  the  Star  Regulus 15 

r>.  Showing  the  Sun  to  be  farther  than  the  Moon 22 

6.  Annular  Eclipsb  of  the  Sun 2(5 

7.  Partial  Eclipse  of  the  Sun 2G 

8.  Eclipse  of  the  Sun,  the  Shadow  of  the  Moon  falling  on  the 

Earth 20 

9.  Eclipse  of  the  Moon,  in  the  Shadow  of  the  Earth 27 

10.  Showing  the  Apparent  Orbit  of  a  Planet 38 

11.  Apparent  Orbits  of  Jupiter  and  Saturn 39 

12.  Arrangement  of  the  Seven  Planets  in  the  Ptolemaic  System...  41 

13.  The  Eccentric 42 

14.  Shoaving    the    Astrological    Division    of    the    Seven    Planets 

AMONG    THE    DaYS    OF    THE    WeEK 46 

15.  Apparent  Annual  Motion  of  the  Sun  explained 55 

16.  Showing  iioav  the  Apparent  Epicyclic  Motion  of  the  Planets 

IS  accounted  for .50 

17.  Relation  of  the  Terrestrial  and  Celestial  Poles  and  Equators.  G2 

18.  Causes  of  Changes  of  Seasons  on  the  Copernican  System G3 

19.  Enlarged  View  cf  the  Earth,  showing  Winter  in  the  North- 

ern Hemisphere,  and  Summer  in  the  Southern 65 

20.  Illustrating  Kepler's  First  Two  Laws  of  Planetary  Motion...  69 

21.  Illustrating  the  Fall  of  the  Moon  towards  the  Earth 78 

22.  Baily's  Apparatus  for  determining  the  Density  of  the  Earth.  83 

23.  View  of  Baily's  Apparatus 84 

24.  Diagram  illustrating  the  Attraction  of  Mountains  85 

25.  Precession  of  the  Equinoxes 88 


Xvi  LIST  OF  ILLUSTBATIOKS. 

ne.  PAGE 

26.  Attractiox  of  the  Moos  tesdisg  to  produce  Tides 91 

27.  Arjollabt  Sphere  as  described  bt  Ptolemy 107 

28.  The  Galilean  Telescope 110 

29.  FoRJiATios  of  as  Image  bt  a  Less Ill 

30.  Great  Telescope  of  the  Sevesteesth  Cestcrt 114 

31.  Refraction  through  a  Compoxtsd  Prism IIG 

32.  Section  of  an  Achromatic  Objective 117 

33.  Section  of  Eve-piece  of  a  Telescope 120 

34.  Mode  of  Mounting  a  Telescope 121 

35.  Speculum  Bringing  Rays  to  a  Single  Focus  bt  Reflection 124 

36.  Herschelias  Telescope 125 

37.  HoKizoxTAL  Section  of  a  Newtonian  Telescope 125 

38.  Section  of  the  Gregorian  Telescope 126 

39.  Herschel's  Great  Telescope 129 

40.  Lord  Rosse's  Great  Telescope 132 

41.  Mr.  Lassell's  Great  Four-foot  Reflector 134 

42.  The  New  Paris  Reflector 136 

43.  The  Great  Melbourne  Reflector 138 

44.  Circles  of  the  Celestial  Sphere 149 

45.  The  Washington  Transit  Circle 155 

4C.  Spider  Lines  in  Field  of  View  of  a  Meridian  Circle 156 

47.  Diagram  illustrating  Parallax 167  g 

48.  Diagram  illustrating  Parallax 168 

49.  Variation  of  Parallax  with  the  Altitude 169 

50.  Apparent  Paths  of  Venus  across  the  Sun 178 

51.  Venus   approaching   Internal    Contact   on   the   Face   of   the 

Sun 180 

52.  Internal  Contact  of  Limb  of  Vescs  with  that  of  the  Sun 180 

53.  The  Black  Drop,  or  Ligament 181 

54.  Method  of  Photogr-^phing  the  Transit  of  Venus 188 

55.  Map  of  the  World,  showing  the  Regions  in  which  the  Tran- 

sit OF  Ven-us  will  be  visible  on  December  Hth,  1882 193 

56.  Effect  of  Stellar  Parallax 200 

57.  Aberration  of  Light 210 

58.  Revolting  Wheel  fob  measuring  the  Velocity  of  Light 214 

59.  Illustratisg  Foucaclts  Method  of  measuring  the  Velocity 

OF  Light 216 

60.  Course  of  Rats  through  a  Spectroscope 222 

61.  Relative  Size  of  Sun  and  Planets 232 

C2.  Orbits  or  the  Planets  from  the  Earth  outward 235 


LIST  OF  ILLUSTBATIOXS.  Xvii 

no.  PASt 

C3.  Aspect  of  the  Sux's  Scetace  as  Photographed  by  Jassses  at 

THE  Obsertatoet  OF  3Iect>os 240 

G4,  C4a.  DisTEiBmos  of  the  Heat  SpECTErsi  as  detebkised  os  Mt. 

Whitxet 250,  251 

65.  Method  of  holding  Telescope,  to  show  Scs  ox  Screes 249 

66.  SoLAE  Spot,  after  Secchi 250 

67.  Chasges  is  the  Aspect  of  a  Solar  Spot  as  it  ceosses  the  Sex's 

Disk 252 

fiS.  Total  Eclipse  of  the  Srs,  as  seen  at  Des  Moises,  Iowa,  Ac- 

GrsT  7th,  1S69 259 

69.  Specimxss  of  Solar  Prottberasces,  as  draws  bt  Secchi 262 

70.  The  Scs,  with  its   Chromosphere  asd  Red  Flajies,  os   July 

23d,  1S71 267 

71.  Illusteatisg  Secchi's  Theory  of  Solar  Spots 275 

72.  Solar  Spot,  after  L.*.sgley 287 

73.  Orbits  of  the  Four  Isser  Plasets,  iLLrsTRATiso  the  Ecces- 

TRICITY   of   those   of   ilERCURY   ASD   MaES 2S9 

74.  Phases  of  Vescs 297 

75.  Showisg  the  Thicksess  of  the  Earth's  Cbust 305 

76.  Distributios  of  Auroras 308 

77.  View  of  Aueoea. 309 

ffS.  SPECTErsf  of  Two  of  the  Great  Auroras  of  1871 311 

79.  Relative  Size  of  Eaeth  asd  Moos 312 

80.  View  of  Moos  sear  the  Third  Quarter 319 

81.  LusAR  Crater  "  Copersicus  "" 321 

82.  The  Plaset  Mars  os  Juke  23d,  1875 328 

83.  Map  of  Maes 328 

84.  Nobthers  Hemisphere  of  Mars 329 

85.  Southers  Hemisphere  of  JL^^rs 329 

85a.  Apparent  Orbits  of  the  Satellites  of  ^Iars  is  1877,  as  ob- 
served  ASD   LAID   DOWS   BY   PROFESSOR   HaLL 331 

86.  Jupiter,  as  sees  with  the  Great  Washisgtos  Telescope,  March 

21sT,  1876 339 

87.  View  of  Jupiter,  as  sees  is  Lord  Rosse's  Great  Telescope, 

February  27th,  1861 341 

88.  View  of  Saturs  ast>  his  Risgs 347 

89.  Specimess  of  Drawisgs  of  Saturs  by  Various  Observers 351 

90.  Views  of  Escke's  Comet  is  1871 375 

91.  Head  of  Dosat^s  Great  Comet  of  1858 376 

92.  Parabolic  asd  Elliptic  Orbit  of  a  Coscet 378 

2 


Xviii  LIST  OF  ILLUSTBATION& 

no.  faor 

93.  Orbit  of  Halley's  Comet 385 

94.  Great  Comet  of  1858 388 

95.  Meteor  Paths,  illustrating  the  Radiant  Point 403 

96.  Orbit  of  November  Meteors  and  the  Comet  of  1861 407 

97.  Orbit  of  the  Second  Comet  of  1862 408 

98.  Measure  of  Position  Angle  of  Double  Star 450 

99.  DisT.o<"CE  OF  Components  of  Double  Star 450 

100.  Diagram  to  illustrate  Position  Angle 4.50 

101.  Telescopic  View  of  the  Pleiades 454 

102.  Cluster  of  47  Toucani 456 

103.  Cluster  u>  Centauri 456 

104.  The  Great  Nebula  of  Orion 458 

105.  The  Annular  Nebula  in  Lyra 460 

106.  The  Omega  Nebula 462 

107.  Nebula  Herschel  3722 463 

108.  The  Looped  Nebula;  Herschel  2941 463 

109.  Herschel's  View  of  the  Form  of  the  Universe 481 

110.  Illustrating  Herschel's  Orders  of  Distance  of  the  Stars....  483 

111.  Probable  Arrangement   of   the  Stars  and   Nebulje  Visible 

WITH  the  Telescope 493 

112.  Diagram  illustrating  Elliptic  Elements  of  a  Plan^et 565 

• 


STAR  MAPS. 

Map      I. — The  Northern  Constellations  withis  60°' 
OF  the  Pole 

"       II. — Southern  Constellations  Visible  in  Au- 
tujen  and  Winter 

"     III. — Southern  Constellations  Visible  in  Win- 
ter AN"D  Spring 

"     IV. — Southern  Constellations  Visible  in  Spring 
AND  Summer ( 

"       V. — Southern  Constellations  Visible  in  Sum- 
mer AND  Autumn J 


yAt  End  of  Book. 


POPULAR  ASTRONOMY. 


PART  L  —  TBE  SYSTEM  OF  THE   WORLD 
HISTORICALLY  DEVELOPED. 


mTRODUCTIOK 


Astronomy  is  the  most  ancient  of  the  physical  sciences,  be 
ing  distinguished  among  them  by  its  slow  and  progressive 
development  from  the  earliest  ages  until  the  present  time. 
In  no  other  science  has  each  generation  which  advanced  it 
'  been  so  much  indebted  to  its  predecessoi-s  for  both  the  facts 
and  the  ideas  necessary  to  make  the  advance.  The  conception 
of  a  globular  and  moving  earth  pursuing  her  course  through 
the  celestial  spaces  among  her  sister  planets,  which  we  see  as 
stars,  is  one  to  the  entire  evolution  of  which  no  one  mind  and 
no  one  age  can  lay  claim.  It  was  the  result  of  a  gradual 
process  of  education,  of  which  the  subject  was  not  an  indi- 
vidual, but  tlie  human  race.  The  great  astronomers  of  all 
ages  have  built  upon  foundations  laid  by  their  predecessors ; 
and  when  we  attempt  to  search  out  the  first  founder,  we  find 
ourselves  lost  in  the  mists  of  antiquity.  The  theory  of  uni- 
versal gravitation  was  founded  by  Newton  upon  the  laws  of 
Kepler,  the  observations  and  measurements  of  his  French  con- 
temporaries, and  the  geometry  of  Apollonius.  Kepler  used 
as  his  material  the  observations  of  Tycho  Brahe,  and  built 
upon  the  theory  of  Copernicus.  When  we  seek  the  origin  of 
the  instruments  used  by  Tycho,  we  soon  find  ourselves  among 


2  SYSTEM  OF  TEE  WORLD  HISTORICALLY  DEVELOPED. 

the  mediaeval  Arabs.  The  discovery  of  the  true  system  of 
the  world  by  Copernicus  was  only  possible  by  a  careful  study 
of  the  laws  of  apparent  motion  of  the  planets  as  expressed  in 
the  epicycles  of  Ptolemy  and  Hipparchus.  Indeed,  the  more 
carefully  one  studies  the  great  work  of  Copernicus,  the  more 
surprised  he  will  be  to  find  how  completely  Ptolemy  furnished 
him  both  ideas  and  material.  If  we  seek  the  teachers  and 
predecessors  of  Hipparchus,  we  find  only  the  shadowy  forms 
of  Egyptian  and  Babylonian  priests,  whose  names  and  writings 
are  all  entirely  lost.  In  the  earliest  historic  ages,  men  knew 
that  tlie  earth  was  round ;  tliat  the  sun  appeared  to  make  an 
annual  revolution  among  the  stars;  and  that  eclipses  were 
caused  by  the  moon  entering  the  shadow  of  the  earth,  or  the 
earth  that  of  the  moon. 

Indeed,  each  of  the  great  civilizations  of  the  ancient  world 
seems  to  have  had  its  own  system  of  astronomy  strongly 
marked  by  the  peculiar  character  of  the  people  among  whom 
it  was  found.  Several  events  recorded  in  the  annals  of  China 
show  that  the  movements  of  the  sun  and  the  laws  of  eclipses 
were  studied  in  that  country  at  a  very  early  age.  Some  of 
these  events  nii.st  be  entirely  mythical ;  as,  for  instance,  the 
despatch  of  astronomers  to  the  four  points  of  the  compass  for 
the  purpose  of  determining  the  equinoxes  and  solstices.  But 
there  is  another  event  which,  even  if  we  place  it  in  the  same 
category,  must  be  regarded  as  indicating  a  considerable  amount 
of  astronomical  knowledge  among  the  ancient  Chinese.  We 
refer  to  the  tragic  fate  of  Hi  and  Ho,  astronomers  royal  to  one 
of  the  ancient  emperors  of  that  people.  It  was  part  of  the 
duty  of  these  men  to  carefully  study  the  heavenly  movements, 
and  give  timely  warning  of  the  approach  of  an  eclipse  or  other 
remarkable  phenomenon.  But,  neglecting  this  duty,  they  gave 
themselves  up  to  drunkenness  and  riotous  living.  In  conse- 
quence, an  eclipse  of  the  sun  occurred  without  any  notice  being 
given ;  the  religious  rites  due  in  such  a  case  were  not  performed, 
and  China  was  exposed  to  the  anger  of  the  gods.  To  appease 
their  wrath,  the  unworthy  astronomers  were  seized  and  sum- 
marily executed  by  royal  command.      Some  historians  have 


INTBODVCIION.  3 

gone  so  far  as  to  fix  the  date  of  this  occurrence,  which  is  vari- 
ously placed  at  from  2128  to  2159  yeai-s  before  the  Christian 
era.  If  this  is  correct,  it  is  the  earliest  of  which  profane  his- 
tory has  left  us  any  record. 

In  the  Hindoo  astronomy  we  see  the  peculiarities  of  the 
contemplative  Hindoo  mind  strongly  reflected.  Here  the 
imagination  revels  in  periods  of  time  which,  by  comparison, 
dwarf  even  the  measures  of  the  celestial  spaces  made  by  mod- 
ern astronomers.  In  this,  and  in  perhaps  other  ancient  sys- 
tems, we  find  references  to  a  supposed  conjunction  of  all  the 
planets  3102  years  before  the  Christian  era.  Although  we 
have  every  reason  for  believing  that  this  conjunction  was 
learned,  not  from  any  actual  record  of  it,  but  by  calculating 
back  the  position  of  the  planets,  yet  the  very  fact  that  they 
were  able  to  make  this  calculation  shows  that  tlie  motions  of 
the  planets  must  have  been  observed  and  recorded  during 
many  generations,  either  by  the  Hindoos  themselves,  or  some 
other  people  from  whom  they  acquired  their  knowledge.  As 
a  matter  of  fact,  we  now  know  from  our  modern  tables  that 
this  conjunction  was  very  far  from  being  exact;  but  its  error 
could  not  be  certainly  detected  by  the  rude  observations  of  the 
times  in  question. 

Among  a  people  so  prone  as  the  ancient  Greeks  to  speculate 
upon  the  origin  and  nature  of  things,  while  neglecting  the  ob- 
servation of  natural  phenomena,  we  cannot  expect  to  find  a.r\y- 
thing  that  can  be  considered  a  system  of  astronomy.  But  there 
are  some  ideas  attributed  to  Pythagoras  which  are  so  frequent- 
ly alluded  to,  and  so  closely  connected  with  the  astronomy  of 
a  subsequent  age,  tliat  we  may  give  them  a  passing  mention. 
He  is  said  to  have  taught  that  the  heavenly  bodies  were  set 
in  a  number  of  crystalline  spheres,  in  the  common  centre  of 
which  the  earth  was  placed.  In  the  outer  of  these  spiieres 
were  set  the  thousands  of  fixed  stars  which  stud  the  firma- 
ment, while  each  of  the  seven  planets  had  its  own  sphere.  The 
transparency  of  each  cr3'stal  sphere  was  perfect,  so  that  the 
bodies  set  in  each  of  the  outer  spheres  were  visible  through 
all  the  inner  ones.     These  spheres  all  rolled  round  on  each 


4         SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

other  ill  a  daily  revolution,  thus  causing  the  rising  and  setting 
of  the  heavenly  bodies.  This  rolling  of  tlie  spheres  on  each 
other  made  a  celestial  music,  the  "  music  of  the  sj)lieres," 
which  filled  the  firmament,  but  was  of  too  elevated  a  char- 
acter to  be  heard  by  the  ears  of  mortals. 

It  must  be  admitted  that  the  idea  of  the  stars  being  set  in  a 
hollow  sphere  of  crystal,  forming  the  vault  of  the  firmament, 
was  a  very  natural  one.  They  seemed  to  revolve  around  the 
earth  every  day,  for  generation  after  generation,  without  the 
slightest  change  in  their  relative  positions.  If  there  were  no 
solid  connection  between  them,  it  does  not  seem  possible  that 
a  thousand  bodies  could  move  around  their  vast  circuit  for 
such  long  periods  of  time  without  a  single  one  of  them  vary- 
ing its  distance  from  one  of  the  others.  It  is  especially  diffi- 
cult to  conceive  how  they  could  all  move  around  the  same 
axis.  But  when  they  are  all  set  in  a  solid  sphere,  eveiy  one  is 
made  secure  in  its  place.  The  planets  could  not  be  set  in  the 
same  sphere,  because  they  change  their  positions  among  the 
stars.  This  idea  of  the  sphericity  of  the  heavens  held  on  to 
the  minds  of  men  with  remarkable  tenacity.  The  funda- 
mental proposition  of  the  system,  both  of  Ptolemy  and  Coper- 
nicus, was  that  the  universe  is  spherical,  the  latter  seeking  to 
prove  the  naturalness  of  the  spherical  form  by  the  analogy 
of  a  drop  of  water,  although  the  theory  served  him  no  pur- 
pose whatever.  Faint  traces  of  the  idea  are  seen  here  and 
there  in  Kepler,  with  whom  it  vanished  from  the  mind  of  the 
race,  as  the  image  of  Santa  Clans  disappears  from  the  mind  of 
the  growing  child. 

Pythagoras  is  also  said  to  have  taught  in  his  esoteric  lect- 
ures that  the  sun  was  the  real  centre  of  the  celestial  move- 
ments, and  that  the  earth  and  planets  moved  around  it,  and  it 
is  this  anticipation  of  the  Copernican  system  which  constitutes 
his  greatest  glor}^  But  he  never  thought  proper  to  make  a 
public  avowal  of  this  doctrine,  and  even  presented  it  to  his 
disciples  somewhat  in  the  form  of  an  hypothesis.  It  must 
also  be  admitted  that  the  accounts  of  his  system  which  have 
reached  us  are  so  vague  and  so  filled  with  metaphysical  specu- 


INTRODUCTION.  5 

lation  that  it  is  questionable  whether  the  frequent  application 
of  his  name  to  the  modern  system  is  not  more  pedantic  than 
justifiable. 

The  Greek  astronomers  of  a  later  age  not  only  rejected  the 
vague  speculations  of  their  ancestors,  but  proved  themselves 
the  most  careful  observers  of  their  time,  and  first  made  astron- 
omy worthy  tlie  name  of  a  science.  From  this  Greek  astrono- 
my the  astronomy  of  our  own  time  may  be  considered  as  com- 
ing by  direct  descent.  Still,  were  it  not  for  the  absence  of  his- 
toric records,  we  could  probably  trace  back  both  their  theories 
and  their  system  of  observation  to  the  plains  of  Chaldea.  The 
zodiac  was  mapped  out  and  the  constellations  named  many 
centuries  before  they  commenced  their  observations,  and  these 
works  marked  quite  an  advanced  stage  of  development.  This 
prehistoric  knowledge  is,  however,  to  be  treated  by  tlie  histo- 
rian rather  than  the  astronomer.  If  we  confine  ourselves  to 
men  whose  names  and  whose  labors  have  come  down  to  us, 
we  must  concede  to  Tlipparchus  the  honor  of  being  the  father 
of  astronomy.  Not  only  do  his  observations  of  the  heavenly 
bodies  appear  to  have  been  far  more  accurate  than  those  of 
any  of  his  predecessors,  but  he  also  determined  the  laws  of  the 
apparent  motions  of  the  planets,  and  prepared  tables  by  which 
these  motions  could  be  calculated.  Probably  he  was  the  first 
propounder  of  the  theory  of  epicyclic  motions  of  the  planets, 
commonly  called  after  the  name  of  his  successor,  Ptolemy,  who 
lived  three  centuries  later. 

Commencing  with  the  time  of  Ilipparchus,  the  general 
theory  of  the  structure  of  the  universe,  or  "system  of  the 
world,"  as  it  is  frequently  called,  exhibits  three  great  stages  of 
development,  each  stage  being  marked  by  a  system  quite  dif- 
ferent from  the  other  two  in  its  fundamental  principles.  These 
are : 

1.  The  so-called  Ptolemaic  system,  which,  however,  really 
belongs  to  Ilipparchus,  or  some  more  ancient  astronomer.  In 
this  system  the  motion  of  the  earth  is  ignored,  and  the  appar- 
ent motions  of  the  stars  and  planets  around  it  are  all  regarded 
as  real. 


6  SYSTEM  OF  THE   WOBLD  HISTORICALLY  DEVELOPED. 

2.  The  Copernican  system,  in  which  it  is  shown  that  the  sun 
is  really  the  centre  of  the  planetary  motions,  and  that  the  earth 
is  itself  a  planet,  both  turning  on  its  axis  and  revolving  round 
the  sun. 

3.  TheXewtonian  system,  in  which  all  the  celestial  motions 
are  explained  by  the  one  law  of  universal  gravitation. 

This  natural  order  of  development  shows  the  order  in  which 
a  knowledge  of  the  structure  of  the  universe  can  be  most 
clearly  presented  to  the  mind  of  the  general  reader.  "VVe 
shall  therefore  explain  this  structure  historically,  devoting  a 
separate  chapter  to  each  of  the  three  stages  of  development 
which  we  have  described.  We  commence  with  what  is  well 
known,  or,  at  least,  easily  seen  by  every  one  who  will  look  at 
the  heavens  with  sufficient  care.  We  imagine  the  observer 
out-of-doors  on  a  starlit  night,  and  show  him  how  the  heav- 
enly bodies  seem  to  move  from  hour  to  hour.  Then,  we  show 
him  what  changes  he  will  see  in  their  aspects  if  he  contin- 
ues his  watch  through  months  and  years.  By  combining  the 
apparent  motions  thus  learned,  he  forms  for  himself  the  an- 
cient, or  Ptolemaic,  system  of  the  world.  Having  this  system 
clearly  in  mind,  the  passage  to  that  of  Copernicus  is  but  a 
step.  It  consists  only  in  showing  that  certain  singular  oscilla- 
tions which  the  sun  and  planets  seem  to  have  in  common  are 
really  due  to  a  revolution  of  the  earth  around  the  sun,  and 
that  the  apparent  daily  revolution  of  the  celestial  sphere  arises 
from  a  rotation  of  the  earth  on  its  own  axis.  The  laws  of 
the  true  motions  of  the  planets  being  perfected  by  Kepler, 
they  are  shown  by  Newton  to  be  included  in  the  one  law  of 
gravitation  towards  the  sun.  Such  is  the  coui-se  of  thought  tc 
wluch  we  first  invite  the  reader. 


TEE  CELESTIAL  SPHERE. 


CHAPTER  I. 

THE   ANCIENT   ASTKONOMY,  OK   THE   APPARENT   MOTIONS   OF   THE 
HEAVENLY   BODIES. 

§  1.  The  Celestial  Sphere. 

It  is  a  fact  with  which  we  are  familiar  from  infancy,  that 
all  the  heavenly  bodies — sun,  moon,  and  stars — seem  to  be  set 
in  an  azure  vault,  which,  rising  high  over  our  heads,  curves 
down  to  the  horizon  on  every  side.  Here  the  earth,  on  which 
it  seems  to  rest,  prevents  our  tracing  it  farther.  But  if  the 
earth  were  out  of  the  way,  or  were  perfectly  transparent,  we 
could  trace  the  vault  downwards  on  every  side  to  the  point 
beneath  our  feet,  and  could  see  sun,  moon,  and  stars  in  every 
direction.  The  celestial  vault  above  us,  with  the  correspond- 
ing one  below  us,  would  then  form  a  complete  sphere,  in  the 
centre  of  which  the  observer  would  seem  to  be  placed.  This 
has  been  known  in  all  ages  as  the  celestial  sphere.  The  direc- 
tions or  apparent  positions  of  the  heavenly  bodies,  as  well  as 
their  apparent  motions,  have  always  been  defined  by  their  sit- 
uation and  motions  on  this  sphere.  The  fact  that  it  is  purely 
imaginary  does  not  diminish  its  value  as  enabling  us  to  form 
distinct  ideas  of  the  directions  of  the  heavenly  bodies  from  us. 

It  matters  not  how  large  we  suppose  this  sphere,  so  long  as 
we  always  suppose  the  observer  to  be  in  the  centre  of  it,  so 
that  it  shall  surround  him  on  all  sides  at  an  equal  distance. 
But  in  the  language  and  reasoning  of  exact  astronomy  it  is 
always  supposed  to  be  infinite,  as  then  the  observer  may  con- 
ceive of  himself  as  transported  to  any  other  point,  even  to  one 
of  the  heavenly  bodies  themselves,  and  still  be,  for  all  practical 
purposes,  in  the  centre  of  the  sphere.  In  this  case,  however, 
the  heavenly  bodies  are  not  considered  as  attached  to  the  cir 
B 


8 


SYSTEM  OF  THE   WORLD  HISTORICALLY  DEVELOPED. 


cumference  of  the  infinite  spliere,  but  only  as  lying  on  tiie  line 
of  sight  extending  from  the  observer  to  some  point  of  the 
sphere.  Their  relation  to  it  may  be  easily  understood  by  the 
observer  conceiving  himself  to  be  luminous,  and  to  throw  out 
rays  in  every  direction  to  tlie  infinitely  distant  sphere.  Then 
the  apparent  positions  of  the  various  heavenly  bodies  will  be 
those  in  which  their  shadows  strike  the  sphere.  For  instance, 
the  observer  standing  on  the  earth  and  looking  at  the  moon;, 


Pig.  1 Section  of  the  imaginary  celestial  ephere.     The  observer  at  0,  looking:  at  the 

stars  or  other  bodies,  marked  p,  q,  r,  s,  t,  u,  v,  will  imagine  them  situated  at  P,  Q,  Ft,  S, 
T,  O,  V,  on  the  surface  of  the  sphere,  where  they  will  appear  projected  along  th3 
straight  pP,  qQ,  etc. 

the  shadow  of  the  latter  will  strike  the  sphere  at  a  point  on  a 
straight  line  drawn  from  the  observer's  eye  through  the  centre 
of  the  moon,  and  continued  till  it  meets  the  sphere.  The  point 
of  meeting  will  i-epresent  the  position  of  the  moon  as  seen  by 
the  observer.  Now,  suppose  the  latter  transported  to  the  moon. 
Then,  looking  back  at  the  earth,  he  will  see  it  projected  on  the 
sphere  in  a  point  diametrically  opposite  to  that  in  Avhich  he 
formerly  saw  the  moon.     To  whatever  planet  he  might  trans- 


THE  DIUBNAL  MOTION.  9 

port  himself,  he  would  see  the  earth  and  the  other  planets  pro- 
jected on  this  imaginary  sphere  precisely  as  we  always  seem 
to  see  the  heavenly  bodies  so  projected. 

This  is  all  that  is  left  of  the  old  crystalline  spheres  of  Py- 
thagoras by  modern  astronomy.  From  being  a  solid  which 
held  all  the  stars,  the  sphere  has  become  entirely  immaterial, 
a  mere  conception  of  the  mind,  to  enable  it  to  define  the  di- 
rections in  which  the  heavenly  bodies  are  seen.  By  examin- 
ing the  figure  it  will  be  clear  that  all  bodies  which  lie  in  the 
same  straight  line  from  the  observer  will  appear  on  the  same 
point  of  the  sphere.  For  instance,  bodies  at  the  three  points 
marked  t  will  all  be  seen  as  if  they  were  at  T. 

§  2.  The  Diurnal  Motion. 

If  we  watch  the  heavenly  bodies  for  a  few  hours  we  shall 
always  find  them  in  motion,  those  in  tlie  east  rising  upwards, 
those  in  the  south  moving  towards  the  west,  and  those  in  the 
west  sinking  below  the  horizon.  We  know  that  this  motion 
is  only  apparent,  arising  from  the  rotation  of  the  earth  on  its 
axis ;  but  as  we  wisli,  in  this  chapter,  only  to  describe  things 
as  they  appear,  we  may  speak  of  the  motion  as  real.  A  few 
days'  watching  will  show  that  the  whole  celestial  sphere  seems 
to  revolve,  as  on  an  axis,  every  day.  It  is  to  this  revolution, 
carrying  the  sun  alternately  above  and  below  the  horizon,  tliat 
the  alternations  of  day  and  night  are  due.  The  nature  and 
effects  of  this  motion  can  best  be  studied  by  watching  the  ap- 
parent movement  of  the  stars  at  night.  We  should  soon  learn 
from  such  a  watch  that  there  is  one  point  in  the  heavens,  or 
on  the  celestial  sphere,  which  does  not  move  at  all.  In  our 
latitudes  this  point  is  situated  in  the  north,  between  the  zenith 
and  the  horizon,  and  is  called  the  pole.  Around  this  pole,  as 
a  fixed  centre,  all  the  heavenly  bodies  seem  to  revolve,  each 
one  moving  in  a  circle,  the  size  of  which  depends  on  the  dis- 
tance of  the  body  from  the  pole.  There  is  no  star  situated 
exactly  at  the  pole,  but  there  is  one  which,  being  situated  lit- 
tle more  than  a  degree  distant,  describes  so  small  a  circle  that 
the  unaided  eye  cannot  see  any  change  of  place  without  mak- 


10       SYSTEM  OF  THE  WORLD  HISTOEICALLY  DEVELOPED. 

ing  some  exact  and  careful  observation.  This  is  therefore 
called  the  pole  star.  The  pole  star  can  nearly  always  be  very 
readily  found  by  means  of  the  pointers,  two  stai"s  of  the  con- 
stellation Ursa  Major,  the  Great  Bear,  or.  as  it  is  familiarly 
called,  the  Dipper.  By  referring  to  the  fignre,  the  reader  will 
readily  find  this  constellation,  by  the  dotted  line  from  the  pole 
and  thence  the  pole  star,  which  is  near  the  centre  of  the  map. 


Fis.  2. — Map  of  the  principal  stars  of  the  northern  sky,  iC'-iwing  the  constellations  which 
never  set  in  latirnde  40=^,  bnt  revolve  round  the  pwle  star  every  day  in  the  direction 
shown  by  the  arrows.  The  two  lower  stars  of  UrM,  Mayjr,  on  the  left  of  the  m^, 
point  to  the  p<de  star  in  the  centre. 

The  altitude  of  the  pole  is  equal  to  the  latitude  of  the  place. 
In  the  Middle  States  the  latitude  is  generally  not  far  from 
forty  degrees ;  the  pole  is  therefore  a  little  nearer  to  the  hori- 
zon than  to  the  zenith.  In  Maine  and  Canada  it  is  about  half- 
way between  these  points,  while  in  England  and  Northern 
Europe  it  is  nearer  the  zenith. 


THE  DIUEXAL  MOTION.  H 

'Novr,  to  see  the  effect  of  the  diurnal  motion  near  the  pole, 
let  us  watch  any  star  in  the  north  between  the  pole  and  the 
horizon.  "We  shall  soon  see  that,  instead  of  moving  from  east 
to  west,  as  we  are  accustomed  to  see  the  heavenly  bodies  move, 
it  really  moves  towards  the  east.  After  passing  the  north 
point,  it  begins  to  cm-ve  its  course  upwards,  until,  in  the  north- 
east, its  motion  is  vertical.  Then  it  turns  gradually  to  the 
west,  passing  as  far  above  the  pole  as  it  did  below  it,  and,  sink- 
ing down  on  the  west  of  the  pole,  it  again  passes  under  it 
The  passage  above  the  pole  is  called  the  upper  culmination, 
and  that  below  it  the  lower  one.  The  course  around  the  pole 
is  shown  by  the  arrows  on  Fig.  2.  AVe  cannot  witli  the  naked 
eve  follow  it  all  the  way  round,  on  account  of  the  intervention 
of  daylight ;  but  by  continuing  our  watch  every  clear  night  for 
a  year,  we  should  see  it  in  every  point  of  its  course.  A  star 
following  the  course  we  have  described  never  sets,  but  may  be 
seen  every  clear  night.  If  we  imagine  a  circle  drawn  round 
the  pole  at  such  a  distance  as  just  to  touch  the  horizon,  all  the 
stars  situated  within  this  circle  will  move  in  this  way ;  this  is 
therefore  called  the  circle  of  perpetual  apparition. 

As  we  go  away  from  the  pole  we  shall  find  the  stars  mov- 
ing in  larger  circles,  passing  higher  up  over  the  \X)\e,  and  lower 
down  below  it,  until  we  reach  the  circle  of  perpetual  appari- 
tion, when  they  will  just  graze  the  horizon.  Outside  this  circle 
every  star  must  dip  below  the  horizon  for  a  greater  or  less 
time,  depending  on  its  distance.  If  it  be  only  a  few  degrees 
outside,  it  will  set  in  the  north-west,  or  between  north  and 
north-west ;  and,  after  a  few  hours  only,  it  will  be  seen  to  rise 
again  between  north  and  north-east,  having  done  little  more 
than  graze  the  horizon.  The  possibility  of  a  body  rising  so 
soon  after  having  set  does  not  always  occur  to  those  who  live 
in  moderate  latitudes.  In  July,  1874,  Coggia's  comet  set  in 
the  north-west  about  nine  o'clock  in  the  evening,  and  rose 
again  about  three  o'clock  in  the  morning ;  and  some  intelligent 
people  who  then  saw  it  east  of  the  pole  supposed  it  could  not 
be  the  same  one  that  had  set  the  evening  before. 

Passing  outside  the  circle  of  perpetual  apparition,  we  find 


12       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

that  the  stars  pass  south  of  the  zenith  at  their  upper  culmina- 
tion, that  they  set  more  quickly,  and  that  they  are  a  longer 
time  below  the  horizon.  This  may  be  seen  in  Fig.  3,  the  por- 
tion of  the  sphere  to  which  we  refer  being  between  the  celes- 
tial equator  and  the  line  ZJT.  When  we  reach  the  equator 
one-half  the  course  will  be  above  and  one-half  below  the  hori- 


FiG.  3.— The  celestial  sphere  iiiid  diurnal  nimiou.  S  is  luc  t..uiii  horizon,  A"  the  m  nh  hori- 
zon, Z  the  zenith.  The  circle  L.V  .irouud  the  north  pole  contains  the  stars  shown  in 
Fig.  2 ;  and  the  obseiTer  at  O,  in  the  centre  of  the  sphere,  looking  to  the  north,  sees  the 
stars  as  they  are  depicted  in  that  figure.  The  .arrows  show  the  direction  of  the  diurnal 
motion  in  the  west. 

zon.  South  of  the  equator  the  circles  described  by  the  stare 
become  smaller  once  more,  and  more  than  half  their  course  is 
below  tlie  horizon.  Near  the  south  horizon  the  stars  only  show 
themselves  above  the  horizon  for  a  sliort  time,  while  below  it 
there  is  a  circle  of  perpetual  disappearance,  the  stars  in  which, 
to  us,  never  rise  at  all.     This  circle  is  of  the  same  magnitude 


MOTION  OF  THE  SUN  AMONG  THE  STARS.  13 

with  that  of  perpetual  apparition,  and  the  south  pole  is  situated 
in  its  centre,  just  as  the  north  pole  is  in  the  centre  of  the  other. 

If  we  travel  southward  we  hnd  that  the  north  pole  gradually 
sinks  towards  the  horizon,  while  new  stars  come  into  view  above 
the  south  horizon ;  consequently  the  circles  of  perpetual  appari- 
tion and  of  perpetual  disappearance  both  grow  smaller.  When 
we  reach  the  earth's  equator  the  south  pole  has  risen  to  the 
south  horizon,  the  north  pole  has  sunk  to  the  north  hori- 
zon ;  the  celestial  equator  passes  from  east  to  west  directly 
overhead ;  and  all  the  heavenly  bodies  in  their  diurnal  revolu- 
tions describe  circles  of  which  one  half  is  above  and  the  other 
half  below  the  horizon.     These  circles  are  all  vertical. 

South  of  the  equator  only  the  south  pole  is  visible,  the  north 
one,  which  we  see,  being  now  below  the  horizon.  Beyond  the 
southern  tropic  the  sun  is  north  at  noon,  and,  instead  of  mov- 
ing from  left  to  right,  its  course  is  from  right  to  left. 

The  laws  of  the  diurnal  motion  which  we  have  described 
may  be  summed  up  as  follows : 

1.  The  celestial  sphere,  with  the  sun,  moon,  and  stars,  seems 
to  revolve  daily  around  an  inclined  axis  passing  through  the 
point  where  we  may  chance  to  stand. 

2.  The  upper  end  of  this  axis  points  (in  this  hemisphere)  to 
the  north  pole ;  the  other  end  passes  into  the  eartli,  and  points 
to  the  south  pole,  which  is  diametrically  opposite,  and  therefore 
below  the  horizon. 

3.  All  the  fixed  stars  during  this  revolution  move  together, 
keeping  at  the  same  distance  from  each  other,  as  if  the  revolv- 
ing celestial  sphere  were  solid,  and  they  were  set  in  it. 

4.  The  circle  drawn  round  the  heavens  half-way  between 
the  two  poles  being  the  celestial  equator,  all  bodies  north  of 
this  equator  perform  more  than  half  their  revolution  above 
the  horizon,  while  south  of  it  less  than  half  is  above  it. 

§  3.  Motion  of  the  Sun  among  the  Stars. 

The  most  obvious  classification  of  the  heavenly  bodies  which 
we  see  with  the  naked  eye  is  that  of  sun,  moon,  and  stars. 
But  there  is  also  this  difference  among  the  stars,  that  while  the 


14       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

great  mass  of  them  preserve  the  same  relative  position  on  the 
celestial  sphere,  year  after  year  and  century  after  century,  there 
are  five  Avhich  constantly  change  their  positions  relatively  to 
the  others.  Their  names  are  Mercury,  Venus,  Mars,  Jupiter, 
and  Saturn.  These  five,  with  the  sun  and  moon,  constitute  the 
seven  planets,  or  wandering  stars,  of  the  ancients,  the  motions 
of  which  are  next  to  he  descrihed.  Taking  out  the  seven 
planets,  the  remaining  heavenly  bodies  visible  to  the  naked 
eye  are  termed  the  Fixed  Stars,  because  they  have  no  appar- 
ent motion,  except  the  regular  diurnal  revolution  described  in 
the  last  section.  But  if  we  note  the  positions  of  the  sun, 
moon,  and  planets  among  the  stars  for  a  number  of  successive 
nights,  we  shall  find  certain  slow  changes  among  them  which 
we  shall  now  describe,  beginning  with  the  sun.  In  studying 
this  description,  the  reader  must  remember  that  we  are  not 
seeking  for  the  apparent  diurnal  motion,  but  onlj^  certain 
much  slower  motions  of  the  planets  relative  to  the  fixed  stai's, 
such  as  would  be  seen  if  the  earth  did  not  rotate  on  its  axis. 

If  we  observe,  night  after  night,  the  exact  hour  and  minute 
at  which  a  star  passes  any  point  by  its  diurnal  revolution,  we 
shall  find  that  passage  to  occur  some  four  minutes  earlier 
every  evening  than  it  did  the  evening  before.  The  starry 
sphere  therefore  revolves,  not  in  24  hours,  but  in  23  hours 
56  minutes.  In  consequence,  if  we  note  its  position  at  the 
same  hour  night  after  night,  we  shall  find  it  to  be  farther  and 
farther  to  the  west.  Let  us  take,  for  example,  the  brightest 
star  in  the  constellation  Leo,  represented  on  Map  III.,  and 
commonly  known  as  Regulus.  If  we  watch  it  on  the  22d  of 
March,  we  shall  find  that  it  passes  the  meridian  at  ten  o'clock 
in  the  evening.  On  April  22d  it  passes  at  eight  o'clock,  and 
at  ten  it  is  two  hours  west  of  the  meridian.  On  the  same  day 
of  May  it  passes  at  six,  before  sunset,  so  that  it  cannot  be  seen 
on  the  meridian  at  all.  When  it  first  becomes  visible  in  the 
evening  twilight,  it  will  be  an  hour  or  more  west  of  the  me- 
ridian. In  June  it  will  be  three  hours  west,  and  by  the  end  of 
July  it  will  set  during  twilight,  and  will  soon  be  entirely  lost 
in  the  rays  of  the  sun.     This  shows  that  during  the  months  in 


MOTION  OF  THE  SUN  AMONG  THE  STARS.  15 

question  the  sun  has  been  approaching  the  star  from  the  west, 
and  in  August  has  got  so  near  it  that  it  is  no  longer  visible. 

Carrying  forward  our  computation,  we  find  tliat  on  August 
21st  the  star  crosses  the  meridian  at  noon,  and  therefore  at 
nearly  the  same  time  with  the  sun.  In  September  it  crosses 
at  ten  in  the  morning,  while  the  sun  is  on  the  eastern  side. 
The  sun  has  therefore  passed  from  the  west  to  the  east  of  the 
star,  and  the  latter  can  be  seen  rising  in  the  morning  twilight 
before  the  sun.  It  constantly  rises  earlier  and  earlier,  and 
therefore  farther  from  the  sun,  until  February,  when  it  rises 
at  sunset  and  sets  at  sunrise ;  and  is  therefore  directly  opposite 
the  sun.  In  March  the  star  would  cross  the  meridian  at  ten 
o'clock  once  more,  showing  that  in  the  course  of  a  year  the 
sun  and  star  had  resumed  their  first  position.  But,  while  the 
sun  has  risen  and  set  365  times,  the  star  has  risen  and  set  366 
times,  the  sun  having  lost  an  entire  revolution  by  the  slow 
backward  motion  we  have  described. 

If  the  stars  were  visible  in  the  daytime  (as  they  would  be 
but  for  the  atmosphere),  the  apparent  motion  of  the  sun  among 
them  could  be  seen  in  the  course  of  a  single  day.  For  in- 
stance, if  we  could  have  seen  Regulus  rise  on  the  morning  of 
August  20th,  1876,  we  should  have  seen  the  sun  a  little  south 
and  west  of  it,  the  relative  position  of  the  sun  being  as  shown 
by  the  circle  numbered  1   in  the  figure.  ^. 

Watching  the  star  all  day,  we  should  find         OTIOO 
that  at  sunset  it  was  north  from  the  sun,  4    s    i    i 

£  •      ^       -\T       ct         rr\-\  1  1    Fio.  4.— Motion  of  the  sua 

as  from  circle  No.  2.  The  sun  would  „a8t  the  .tar  Kegnius 
during  the  day  have  moved  nearly  its  own  a^ont  August  26th  of 
diameter.  Next  morning  we  should  have  ^  ^^^ 
seen  that  the  sun  had  gone  past  the  star  into  position  3,  so 
that  the  lattei*  would  now  rise  before  the  former.  By  sun- 
set it  would  have  advanced  to  position  4,  and  so  forth.  The 
path  which  the  sun  describes  among  the  stars  in  his  annual 
revolution  is  called  the  ecliptic.  It  is  m.arked  down  on  Maps 
II.,  III.,  IV.,  and  v.,  and  the  months  in  which  the  sun  passes 
through  each  portion  of  the  ecliptic  are  also  indicated.  A 
belt  of  the  heavens,  extending  a  few  degrees  on  each  side  of 

3 


16       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

the  ecliptic,  is  called  the  zodiac.  The  poles  of  the  ecliptic  are 
two  opposite  points,  each  in  the  centre  of  one  of  the  two  hemi- 
spheres into  which  the  ecliptic  divides  the  celestial  sphere. 

The  determination  of  the  solar  motion  aronnd  the  ecliptic 
may  be  considered  the  birth  of  astronomical  science.  The 
prehistoric  astronomers  divided  the  ecliptic  and  zodiac  into 
twelve  parts,  now  familiarly  known  as  the  signs  of  the  zodiac. 
This  proceeding  was  probably  snggested  by  the  needs  of  agii- 
cultnre,  and  of  the  chronological  reckoning  of  yeai"S.  A  very 
little  observation  would  show  that  the  changes  of  the  seasons 
are  due  to  the  variations  in  the  meridian  altitude  of  the  sun, 
and  in  the  length  of  the  da}' ;  but  it  was  only  by  a  careful 
study  of  the  position  of  the  ecliptic,  and  the  motion  of  the  sun 
in  it,  that  it  could  be  learned  how  these  variations  in  the  daily 
course  of  the  sun  M-ere  brought  about.  This  study  showed 
that  they  were  due  to  the  fact  that  the  ecliptic  and  equator 
did  not  coincide,  but  were  inclined  to  each  other  at  an  angle 
of  between  twenty-three  and  twenty-four  degrees.  This  in- 
clination is  known  as  the  obliquity  of  the  ecliptic.  The  two 
circles,  equator  and  ecliptic,  cross  each  other  at  two  opposite 
points,  the  positions  of  which  among  the  stars  may  be  seen  by 
reference  to  Maps  II. -V.  When  the  sun  is  at  either  of 
these  points,  it  rises  exactly  in  the  east,  and  sets  exactly  in  the 
■west ;  one-half  its  diurnal  course  is  above  the  horizon,  and  the 
other  half  below.  The  days  and  nights  are  therefore  of  equal 
length,  from  which  the  two  points  in  question  are  called  the 
J^(jui7ioxes. 

The  vernal  equinox  is  on  tlie  right-hand  edge  of  Map  II. 
Leaving  that  equinox  about  March  21st,  the  sun  crosses  over 
the  region  represented  by  the  map  in  the  coui-se  of  the  next 
three  months,  working  northward  as  it  does  so,  until  June  20th, 
when  it  is  on  the  left-hand  edge  of  the  map,  23^°  north  of  the 
equator.  This  point  of  the  ecliptic  is  called  the  summer  solstice, 
being  that  in  which  the  sun  attains  its  greatest  northern  declina- 
tion. When  near  this  solstice,  it  rises  north  of  east,  culmi- 
nates at  a  high  altitude  (in  our  latitudes),  and  sets  north  oi 
west.     As  explained  in  describing  the  diurnal  motion  of  an 


MOTION  OF  THE  SUN  AMONG  THE  STARS.  17 

object  north  of  tlie  celestial  equator,  more  than  half  the  daily 
course  of  the  sun  is  now  above  our  horizon,  so  that  our  days 
are  longer  than  our  nights,  while  the  great  meridfan  altitude 
of  the  sun  produces  the  heats  of  summer. 

The  portion  of  tlie  ecliptic  represented  on  Map  II.,  com- 
mencing at  the  vernal  equinox,  where  the  sun  crosses  the  equa- 
tor, was  divided  by  the  early  astronomer  into  the  three  signs 
of  Aries,  the  Ram  ;  Taurus,  the  Bull ;  and  Gemini,  the  Twins. 
It  will  be  seen  that  these  signs  no  longer  coincide  witli  the 
constellations  of  the  same  name :  this  is  owing  to  a  change  in 
the  position  of  the  equator,  which  will  be  described  presently. 

Turning  to  Map  III.,  we  see  that  during  the  three  months, 
from  June  to  Septembei",  the  sun  works  downwards  towards 
the  equator,  reaching  it  about  September  20th.  The  point  of 
crossing  marks  the  autumnal  equinox,  found  also  on  the  right 
hand  of  Map  lY.  The  days  and  nights  are  now  once  more  of 
equal  length. 

During  the  next  six  months  the  sun  is  passing  over  the  re- 
gions represented  on  Maps  IV,  and  Y.,  and  is  south  of  the 
equator,  its  greatest  soutliern  declination,  or  "  the  southern 
solstice,"  being  reached  about  December  21st.  More  than 
half  its  daily  course  is  then  below  the  horizon,  so  that  in  our 
latitudes  the  nights  are  longer  than  the  da3's,  and  the  low 
noonday  altitude  of  the  sun  gives  rise  to  the  colds  of  winter. 

We  have  no  historic  record  of  this  division  of  the  zodiac 
into  signs,  and  the  ideas  of  the  authors  can  only  be  inferred 
from  collateral  circumstances.  It  has  been  fancied  that  the 
names  were  suggested  by  the  seasons,  the  agricultural  opera- 
tions, and  so  on.  Thus  the  spring  signs  (Aries,  the  Ram ;  Tau- 
rus, the  Bull;  and  Gemini,  the  Twins)  are  supposed  to  mark  the 
bringing  forth  of  young  by  the  flocks  and  herds.  Cancer,  the 
Crab,  marks  the  time  when  the  sun,  having  attained  its  great- 
est declination,  begins  to  go  back  towards  the  equator;  and  the 
crab  having  been  supposed  to  mo\'e  backwards,  his  name  was 
given  to  this  sign.  Leo,  the  Lion,  symbolizes  the  fierce  heat 
of  summer;  and  Yii-go,  the  Yirgin,  gleaning  corn,  symbolizes 
the  harvest.     In  Libra,  the  Balance,  the  day  and  night  balance 


18       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

eacli  other,  being  of  equal  length.  Scorpius,  the  Scorpion,  is 
supposed  to  have  marked  the  presence  of  venomous  reptiles  ni 
October ;  while  Sagittarius,  the  Archer,  symbolizes  the  seasoii 
of  hunting.  The  explanation  of  Capricornns,  the  Goat,  is  more 
fanciful,  if  possible,  than  that  of  Cancer.  It  was  supposed  that 
this  animal,  ascending  the  hill  as  he  feeds,  in  order  to  reach 
the  grass  more  easily,  on  reaching  the  top,  turns  back  again,  so 
that  his  name  was  used  to  mark  the  sign  in  which  the  sun, 
from  going  south,  begins  to  return  to  the  north.  Aquarius, 
the  Water-bearer,  symbolizes  the  winter  rains;  and  Pisces,  the 
Fishes,  the  season  of  fishes. 

All  this  is,  however,  mere  conjecture;  the  only  coincidences 
at  all  striking  being  Virgo  and  Libra.  The  names  of  the  con- 
stellations were  probably  given  to  them  several  centuries,  per- 
haps even  thousands  of  years,  before  the  Christian  era ;  and  in 
that  case  the  zodiacal  constellations  would  not  have  correspond- 
ed to  the  seasons  we  have  indicated.  An  attempt  has  even  been 
made  to  show  that  the  names  of  the  zodiacal  constellations  were 
intended  to  commemorate  the  twelve  labors  of  Hercules;  but 
this  theory  rests  on  no  better  foundation  than  the  other. 

The  zodiacal  constellations  occupy  quite  unequal  spaces  in 
the  heavens,  as  may  be  seen  by  inspection  of  the  maps.  In 
the  beginning  they  were  simply  twelve  houses  for  the  sun, 
which  that  luminary  occupied  in  the  course  of  the  year.  Tlip- 
parchus  found  this  system  entirely  insufficient  for  exact  astron- 
omy, and  therefore  divided  the  ecliptic  and  zodiac  into  twelve 
equal  parts,  of  30°  each,  called  signs  of  the  zodiac.  He  gave 
to  these  signs  the  names  of  the  constellations  most  nearly  cor- 
responding to  them.  Commencing  at  the  vernal  equinox,  the 
first  arc  of  30°  was  called  the  sign  Aries,  the  second  the  sign 
Taurus,  and  so  forth.  The  mode  of  reckoning  positions  on 
the  ecliptic  by  signs  was  continued  until  the  last  century',  but 
is  no  longer  in  use  among  professional  astronomers,  owing  to 
its  inconvenience.  The  whole  ecliptic  is  now  divided  into 
360°,  like  any  other  circle,  the  count  commencing  at  the  vernal 
equinox,  and  following  the  direction  of  the  sun's  motion  all  the 
way  round  to  360°. 


PRECESSION  OF  THE  EQUINOXES.  19 

^  4.  Precession  of  the  Equinoxes. — The  Solar  Year. 

By  comparing  his  own  observations  with  those  of  preceding 
astronomers,  Hipparchns  found  that  the  equinoxes  were  slowly 
shifting  their  places  among  tlie  stars,  the  change  being  at  least 
a  degree  in  a  century  towards  the  west.  His  successors  deter- 
mined it  with  greater  exactness,  and  it  is  now  known  to  be 
nearly  a  degree  in  seventy  years.  Careful  study  of  the  cliange 
shows  that  it  is  due  mainly  to  a  motion  of  the  equator,  which 
again  arises  from  a  change  in  the  direction  of  the  pole.  Tlie 
position  of  the  ecliptic  among  the  stars  varies  so  slowly  that  tlie 
change  can  be  seen  only  by  the  refined  observations  of  modern 
times.  In  the  explanation  of  the  diurnal  motion,  it  was  stated 
that  there  was  a  certain  point  in  tlie  heavens  around  which  all 
the  heavenly  bodies  seem  to  perform  a  daily  revolution.  This 
point,  the  pole  of  the  heavens,  is  marked  on  the  centre  of  Map 
I.,  and  is  also  in  the  centre  of  Fig.  2,  page  10.  It  is  little  more 
than  a  degree  distant  from  the  pole  star.  Now,  precession  real- 
ly consists  in  a  very  slow  motion  of  this  pole  around  tlie  pole 
of  the  ecliptic,  the  rate  of  motion  being  such  as  to  carry  it  all 
the  way  round  in  about  25,300  years.  The  exact  time  has 
never  been  calculated,  and  would  not  always  be  the  same,  ow- 
ing to  some  smpU  variations  to  which  the  motion  is  subject; 
but  it  will  never  differ  much  from  this.  There  is  a  very  slight 
motion  to  the  ecliptic  itself, and  therefore  to  its  pole;  and  this 
fact  renders  the  motion  of  the  pole  of  the  equator  around  it 
somewhat  complicated ;  but  the  eurve  described  by  the  latter 
is  very  nearly  a  circle  46°  in  diameter.  In  the  time  of  Ilip- 
parchus,  our  present  pole  star  was  12°  from  the  pole.  The  pole 
has  been  approaching  it  steadily  ever  since,  and  will  continue 
to  approach  it  till  about  the  year  2100,  when  it  will  slowly 
pass  by  it  at  the  distance  of  less  than  half  a  degree.  The 
course  of  the  pole  during  the  next  12,000  years  is  laid  down 
on  the  map,  and  it  will  be  seen  that  at  the  end  of  that  time 
it  will  be  near  the  constellation  Lyra,  Since  the  equator  is 
always  90°  distant  from  the  pole,  there  will  be  a  correspond- 
ing motion  to  it,  and  hence  to  the  point  of  its  crossing  the 


20       SYSTEM  OF  THE  WOELD  HISTORICALLY  DEVELOPED. 

ecliptic.  To  show  this,  the  position  of  tlie  equator  2000  3-ears 
ago,  as  well  as  its  present  position,  is  given  on  Map  II. 

The  reader  will,  of  coui-se,  understand  that  the  various  ce- 
lestial movements  of  which  we  have  spoken  in  this  chapter  are 
only  apparent  motions,  and  are  due  to  the  motion  of  the  earth 
itself,  as  will  be  explained  in  the  chapter  on  the  Coperuican 
system.  The  diurnal  revolution  of  the  celestial  sphere  is  due 
to  the  rotation  of  the  earth  on  its  axis,  while  precession  is  real- 
ly a  change  in  the  direction  of  that  axis. 

One  important  effect  of  precession  is  that  one  revolution  of 
the  sun  among  the  stars  does  not  accurately  correspond  to  the 
return  of  the  same  seasons.  The  latter  depend  upon  the  posi- 
tion of  the  sun  relative  to  the  equinox,  the  time  when  the  sun 
crosses  the  equator  towards  the  north  always  marking  the  sea- 
son of  spring  (in  the  northern  hemisphere),  no  matter  where 
the  sun  may  be  among  the  stars.  If  the  equator  did  not  move, 
the  sun  would  always  ci-oss  it  at  nearly  the  same  point  among 
the  stars.  But  when,  starting  from  the  vernal  equinox,  it 
makes  the  circuit  of  the  heavens,  and  returns  to  it  again,  the 
motion  of  the  equator  has  been  such  that  the  sun  crosses  it 
20  minutes  before  it  reaches  the  same  star.  In  one  year,  tin's 
difference  is  very  small ;  but  by  its  constant  accumulation,  at 
the  i"ate  of  20  minutes  a  year,  it  becomes  very  considerable 
after  the  lapse  of  centuries.  We  must,  therefore,  distinguish 
between  the  sidereal  and  the  tropical  year,  the  former  l)eing 
the  period  required  for  one  revolution  of  the  sun  among  tlie 
stars,  the  latter  that  required  for  his  return  to  the  same  equi- 
nox, whence  it  is  also  called  the  equinoctial  year.  The  exact 
lengths  of  these  respective  years  are  : 

Days.  Days.    Honn.    Hid.      Sec 

Sidereal  year 3G:i.  25636  =  365       6        9       9 

Tropical  ye-nr 365.24220  =  365       5      48     46 

Since  the  recurrence  of  the  seasons  depends  on  the  tropical 
year,  the  latter  is  the  one  to  be  used  in  forming  the  calendar, 
and  for  the  purposes  of  civil  life  generally.  Its  true  length  is 
11  minutes  11  seconds  less  tlian  365J  days.  Some  results  of 
this  difference  will  be  shown  in  explaining  the  calendar. 


THE  MOOX.  21 

§  5.  The  Mooti's  Motion. 

Every  one  knows  that  the  moon  makes  a  revolution  in  the 
{'.elesdal  sphere  in  ahout  a  month,  and  that  during  its  revohi- 
tion  it  presents  a  number  of  different  phases,  known  as  '*  new 
moon,"  "first  quarter,"  "full  moon,"  and  so  on,  depending 
on  its  position  relative  to  the  sun.  A  study  of  these  phases 
during  a  single  revolution  will  make  it  clear  that  the  moon  is 
a  globular  dark  body,  illuminated  by  the  light  of  the  sun,  a 
fact  which  has  been  evident  to  careful  observei^  from  the  re- 
motest antiquity.  This  may  be  illustrated  by  taking  a  large 
globe  to  represent  the  moon,  painting  one  half  white,  to  rep- 
resent the  half  on  which  the  sun  shines,  and  the  other  half 
dark.  Viewing  it  at  a  proper  distance,  and  turning  it  into 
different  positions,  it  will  be  found  that  the  visible  part  of  the 
white  half  may  be  made  to  imitate  the  various  appearances  of 
the  moon. 

As  the  sun  makes  a  revolution  around  the  celestial  sphere 
in  a  year,  so  the  moon  makes  a  similar  revolution  among  the 
stars  in  a  little  more  than  27  days.  This  motion  can  be  seen 
on  any  clear  night  between  tirst  quarter  and  full  moon,  if  the 
moon  happens  to  be  near  a  bright  star.  If  the  position  of  the 
moon  relatively  to  the  star  be  noted  fi-om  hour  to  hour,  it  will 
be  found  that  she  is  constantly  working  towards  the  east  by  a 
distance  equal  to  her  own  diameter  in  an  hour.  The  follow- 
ing night  she  will  be  found  from  12°  to  14°  east  of  the  star, 
and  will  rise,  cross  the  meridian,  and  set  from  half  an  hour  to 
an  hour  later  than  she  did  the  preceding  night.  At  the  end 
of  27  days  S  houi-s,  she  will  be  back  in  the  same  position 
among  the  stars  in  which  she  was  fii-st  seen. 

If,  however,  starting  from  one  new  moon,  we  count  forwards 
this  period,  we  shall  find  that  the  moon,  although  she  has  re- 
turned to  the  same  position  among  the  stars,  has  not  got  back 
to  new  moon  again.  The  reason  is  that  the  sun  has  moved 
forwards,  in  virtue  of  his  apparent  annual  motion,  so  far  that 
it  will  require  more  than  two  days  for  the  moon  to  overtake 
bim.     So,  although  the  moon  really  revolves  around  the  earth 


23        SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

in  27^  days,  the  average  interval  between  one  new  moon  and 
the  next  is  29^  days. 

A  comparison  of  the  phases  of  the  moon  with  her  direction 
will  show  that  the  sun  is  many  times  more  distant  than  the 
moon.  In  Fig.  5,  let  £  be  the  position  of  an  observer  on  the 
earth,  JVthe  moon,  and  6"  the  sun,  illuminating  one  half  of  it. 
^Vllen  tlie  observer  sees  the  moon  in  her  fii-st  quarter — that  is, 
when  her  disk  appears  exactly  half  illuminated — the  angle  at 


j/e- 


r\ 


Fig.  6. — Showing  the  sau  to  be  farther  th.ui  the  moon. 

the  moon,  between  the  observer  and  the  sun,  must  be  a  right 
angle.  If  the  sun  were  only  about  four  times  as  far  as  the 
moon,  as  in  the  tigure,  tlie  observer,  by  measuring  the  angle 
xS^'J/^  between  the  sun  and  moon,  would  tind  it  to  be  75°  ;  and 
the  nearer  the  sun,  the  smaller  he  would  tind  it.  But  actual 
measurement  would  show  it  to  be  so  near  90°  that  the  dif- 
ference would  be  imperceptible  with  ordinary  instruments. 
Hence,  the  sun  is  really  at  the  point  where  the  dotted  line  and 
the  line  JIS  continued  meet  each  other,  which  is  many  times 
the  distance  EM  to  the  moon. 

This  idea  was  applied  by  Aristarchus,  wlio  flourished  in  the 
third  century  before  Cln-ist,  preceding  both  Hipparchus  and 
Ptolemy,  to  determine  the  distance  of  the  sun,  or,  more  ex- 
actly, how  many  times  it  exceeded  the  distance  of  the  moon. 
He  found,  by  measurement,  that,  in  the  position  represented 
in  the  tigure,  the  distance  between  the  directions  of  the  sun 
and  moon  was  87°,  and  that  the  sun  was  therefore  something 
like  twenty  times  as  far  as  tlie  moon.  AVe  now  know  that  this 
result  was  twenty  times  too  small,  the  angle  being  really  so 
near  90°  that  Aristarchus  could  not  determine  the  difference 
with  certainty.     In  principle,  the  method  is  quite  correct,  and 


THE  MOON.  23 

very  ingenious,  but  it  cannot  be  applied  in  practice.  Tlie  one 
insuperable  difficulty  of  the  method  arises  from  the  impossi- 
bility of  seeing  when  the  moon  is  exactly  half  illuminated. 
the  uncertainty  arising  from  tlie  inequalities  in  the  lunar  sur- 
face being  greater  than  the  whole  angle  to  be  measured. 

Watching  and  mapping  down  the  path  of  the  moon  among 
the  stars,  it  is  found  not  to  be  the  same  with  that  of  the  sun, 
being  inclined  to  it  about  5°.  The  paths  cross  each  other  in 
two  opposite  points  of  the  heavens,  called  the  moon's  nodes. 
The  path  of  the  moon  in  the  middle  of  the  year  1877  is 
marked  on  star  Maps  II.- V.  Referring  to  Map  III.,  it  will 
be  seen  that  the  descending  node  of  the  moon  is  in  the  con- 
stellation Leo,  very  near  the  star  Regulus.  Here  the  moon 
passes  south  of  or  TdcIow  the  ecliptic,  and  continues  below  it 
over  the  whole  of  Map  IV.  On  Map  Y.,  it  approaches  the 
ecliptic  again,  crossing  to  the  north  of  it  in  the  constellation 
Aquarius,  and  continuing  on  that  side  till  it  reaches  Regulus 
once  more. 

Such  is  the  moon's  path  in  July,  1877.  But  it  is  con- 
stantly changing  in  consequence  of  a  motion  of  the  nodes 
towards  the  west,  amounting  to  more  than  a  degree  in  every 
revolution.  In  order  that  the  line  drawn  on  the  map  may 
continue  to  represent  the  path  of  the  moon,  we  must  suppose 
it  to  slide  along  the  ecliptic  towards  the  right  at  the  rate  of 
about  20°  a  year,  so  that  a  slightly  different  path  will  be  de- 
scribed in  every  monthly  revolutioii.  The  path  will  always 
cross  the  ecliptic  at  the  same  angle,  but  the  moon  will  not 
always  pass  over  the  same  stars.  In  August,  1877,  she  will 
cross  the  ecliptic  a  little  farther  to  the  right  (west),  and  will 
pass  a  little  below  Regulus.  The  change  going  on  from 
month  to  month  and  from  year  to  year,  in  a  little  less  than 
ten  years  the  ascending  node  will  be  found  in  Leo;  and  the 
other  node,  now  in  Leo,  will  have  gone  back  to  Aquarius. 
In  a  period  of  eighteen  years  and  seven  months,  the  nodes 
will  have  made  a  complete  revolution,  and  the  path  of  the 
moon  will  have  resumed  the  position  given  on  the  map. 


24       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOFED. 

§  6.  Eclipses  of  the  Sun  and  Moon. 

Tlie  early  inhabitants  of  the  woi'ld  were,  no  doubt,  terrified 
by  tiie  occasional  recurrence  of  eclipses  many  ages  before 
there  were  astronomers  to  explain  tlieir  causes.  But  the  mo- 
tions of  the  sun  and  moon  could  not  be  observed  very  long 
without  the  causes  being  seen.  It  was  evident  that  if  the 
moon  should  ever  chance  to  pass  between  the  earth  and  the 
sun,  she  must  cut  off  some  or  all  of  his  light.  If  the  two  bodies 
followed  the  same  track  in  the  heavens,  there  would  be  an 
eclipse  of  the  sun  every  new  moon  ;  but,  owing  to  the  incli- 
nation of  the  two  orbits,  the  moon  will  generally  pass  above 
or  below  the  sun,  and  there  will  be  no  eclipse.  If,  however, 
the  sun  happens  to  be  in  the  neighborhood  of  the  moon's  node 
when  the  moon  passes,  then  there  will  be  an  eclipse.  For  an 
example,  let  us  refer  to  Map  III.  We  see  that  the  sun  passes 
the  moon's  descending  node  about  August  25th,  1877,  and  is 
within  20°  of  this  node  from  early  in  August  till  the  middle 
of  September.  The  moon  passes  the  sun  on  August  Stli  and 
September  6th  of  that  yeai-,  M-hich  are,  therefore,  the  dates  of 
new  moon.  At  the  first  date,  the  moon  passes  so  far  to  the 
north  that,  as  seen  from  the  centre  of  the  earth,  there  is  no 
eclipse  at  all ;  but  in  the  northern  part  of  Asia  the  moon 
would  be  seen  to  cut  off  a  small  portion  of  the  sun. 

While  the  moon  is  performing  another  circuit,  the  sun  has 
moved  so  far  past  the  node,  that  the  moon  passes  south  of  it, 
and  there  is  only  a  small  eclipse,  and  that  is  visible  only 
around  the  region  of  Cape  Horn.  Thus,  there  are  two  solar 
eclipses  while  the  sun  is  passing  this  node  in  1877,  but  both 
are  very  small.  Indeed,  every  time  the  sun  crosses  a  node, 
the  moon  is  sure  to  cross  his  path,  either  befoi'e  he  reaches 
the  node,  or  before  he  gets  far  enough  from  it  to  be  out  of 
the  way.  As  he  crosses  both  nodes  in  the  course  of  the  year, 
there  must  be  at  least  two  solar  eclipses  every  year  to  some 
points  of  the  earth's  surface. 

The  cause  of  lunar  eclipses  might  not  have  been  so  easy  to 
guess  as  was  that  of  solar  ones ;  but  a  great  number  could 


ECLIPSES  OF  THE  SUN  AND  MOON.  25 

not  have  been  observed,  and  their  times  of  occurrence  record- 
ed, without  its  being  noticed  that  they  always  occurred  at  full 
moon,  when  tlie  earth  was  ojjposite  tlie  sun.  The  idea  tliat 
the  earth  cast  a  shadow,  and  tliat  the  moon  passed  into  it, 
conld  then  hardly  fail  to  suggest  itself ;  and  we  find,  accord- 
ingly, that  the  earliest  observers  of  the  heavens  were  perfectly 
acquainted  with  the  cause  of  lunar  eclipses. 

Tlie  reason  why  eclipses  of  the  moon  only  occur  occasion- 
ally is  of  the  same  general  nature  with  that  of  the  rare  occur- 
rence of  solar  eclipses.  The  centre  of  the  earth's  shadow  is 
always,  like  the  sun,  in  the  ecliptic ;  and  unless  the  moon  hap- 
pens to  be  very  near  the  ecliptic,  and  therefore  very  near  one 
of  her  nodes  at  the  time  of  full  moon,  she  will  fail  to  strike 
the  shadow,  passing  above  or  below  it.  Owing  to  the  great 
magnitude  of  tiie  sun,  the  earth's  shadow  is,  at  the  distance  of 
the  moon,  much  smaller  than  the  earth  itself.  The  result  of 
this  is,  that  the  moon  must  be  decidedly  nearer  her  node  to 
produce  a  lunar  than  to  produce  a  solar  eclipse.  Sometimes 
a  wliole  year  passes  without  there  being  any  eclipse  of  the 
moon. 

The  nature  of  an  eclipse  will  vary  with  the  positions  and 
apparent  magnitudes  of  the  sun  and  moon.  Let  us  suppose, 
first,  that,  in  a  solar  eclipse,  the  centre  of  the  moon  happens 
to  pass  exactly  over  the  centre  of  the  sun.  Then,  it  is  clear 
that  if  the  apparent  angular  diameter  of  the  moon  exceed  that 
of  the  sun,  the  latter  will  be  entirely  hidden  from  view.  This 
is  called  a  total  eclipse  of  the  sun.  It  is  evident  that  such  an 
eclipse  can  occur  only  when  the  observer  is  near  the  line  join- 
ing the  centres  of  the  sun  and  moon.  If,  under  the  same  cir- 
cumstances, the  apparent  magnitude  of  the  moon  is  less  than 
that  of  the  sun,  it  is  evident  that  the  whole  of  the  latter  cannot 
be  covered,  but  a  ring  of  light  around  his  edge  will  still  be  visi- 
ble. This  is  called  an  annular  eclipse.  If  the  moon  does  not 
pass  centrally  over  the  sun,  then  it  can  cover  only  a  portion  of 
the  latter  on  one  side  or  the  other,  and  the  eclipse  is  said  to  be 
partial.  So  with  the  moon  :  if  the  latter  is  only  partially  ir.i- 
mersed  in  the  earth's  shadow,  the  eclipse  of  the  moon  is  called 


20        SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

partial ;  if  she  is  totally  imiiiei'sed  in  it,  so  that  no  direct  sun- 
light can  reach  her,  the  eclipse  is  said  to  be  total.     An  au- 


FiG.  C— Auuular  eclipse  of  the  son. 


Fig.  T. — Partial  eclipse  of  ilie  sun. 


niilar  eclipse  of  the  moon  is  impossible,  because  the  earth's 
shadow  always  exceeds  the  diameter  of  the  moon  in  breadth. 

Sonic  points  respecting  eclipses  will  be  seen  more  clearly 
by  reference  to  the  accompanying  figures,  in  which  S  repre- 
sents the  sun,  E  the  earth,  and  J/ the  moon.  Referring  to  the 
first  figure,  it  will  be  seen  that  an  observer  at  either  of  the 
points  marked  O,  or  indeed  anywhere  outside  the  shaded  por- 
tions, will  see  the  whole  of  the  sun,  so  that  to  liiin  there  will 
be  no  eclipse  at  all.  Within  the  lightly  shaded  regions,  marked 
PP.  the  sun  will  be  partially  eclipsed,  and  more  so  as  the  ob- 
server is  near  the  centre.    This  region  is  called  the  penumbra. 


Fig.  S. — Eclipse  of  tlie  suu,  the  shadow  of  the  moou  falliug  on  the  earth. 

Within  the  darkest  parts  between  the  two  letters  P  is  a  region 
where  the  sun  is  totally  hidden  by  the  moon.  This  is  the 
shadow,  and  its  form  is  that  of  a  cone,  with  its  base  on  the 
moon,  and  its  point  extending  towards  the  earth.  Now,  it 
happens  that  the  diameters  of  the  sun  and  moon  are  very 
nearly  proportional  to  their  respective  mean  distances,  so  that 
the  point  of  this  shadow  almost  exactly  reaches  the  surface  of 
th3  earth.  Indeed,  so  near  is  the  adjustment,  that  the  dark 
shadow  sometimes  reaches  the  earth,  and  sometimes  does  not. 


ECLIPSES  OF  THE  SUN  AND  MOON. 


27 


owing  to  the  small  changes  in  the  distance  of  the  sun  and 
moon.  When  the  shadow  reaches  the  earth,  it  is  comparative- 
ly very  narrow,  owing  to  its  being  so  near  its  sharp  point ;  but 
if  an  observer  can  station  himself  within  it,  he  will  see  a  total 
eclipse  of  the  snn  during  the  short  time  the  shadow  is  passing 
over  him.  If  the  reader  will  study  the  figure,  he  will  see  why 
a  total  eclipse  of  the  sun  is  so  rare  at  any  one  place  on  the 
earth.  The  shadow,  when  it  reaches  the  earth,  is  so  near  down 
to  a  point  that  its  diameter  is  not  generally  more  than  a  hun- 
dred miles ;  consequently,  eacli  total  eclipse  is  visible  only 
along  a  belt  which  may  not  average  more  than  a  hundred 
miles  across. 

In  most  eclipses,  the  shadow  comes  to  a  point  before  it 
reaches  the  earth ;  in  this  case,  the  apparent  angular  diameter 
of  the  moon  is  less  than  that  of  the  sun,  and  there  can  be  no 
total  eclipse.  But  if  an  observer  places  himself  in  a  line  witli 
the  centre  of  the  shadow,  he  will  see  an  annular  eclipse,  the 
sun  showing  itself  on  all  sides  of  the  moon. 

The  next  fiarure  shows  ns  the  form  of  the  earth's  shadow. 


Fio.  9.— Eclipse  of  the  moon,  the  Intter  being  in  the  shadow  of  the  earth. 

The  earth  being  much  larger  than  the  moon,  its  shadow  ex- 
tends far  beyond  it;  and  where  it  reaches  the  moon,  it  is  al- 
ways so  much  larger  than  the  latter  that  she  may  be  wholly 
immersed  in  it,  as  shown  in  the  figure.  Now,  suppose  the 
moon,  in  her  course  round  the  earth,  to  pass  centrally  through 
the  shadow,  and  not  above  or  below  it,  as  she  commonly  does ; 
then,  when  she  entered  the  shaded  region,  marked  P,  which 
is  called  the  penumbra,  an  observer  on  her  surface  would  see 
a  partial  eclipse  of  the  sun  caused  by  the  intervention  of  the 


28        SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

earth.  The  time  when  this  begins  is  given  in  the  ahnanacs, 
being  expiessed  by  the  words,  "  Moon  enters  penumbra." 
Some  of  tlie  sunlight  is  then  cut  off  from  the  moon,  so  that 
the  latter  is  not  so  bright  as  usual ;  but  the  eye  does  not 
notice  any  loss  of  light  until  the  moon  almost  reaches  the 
dark  shadow.  As  she  enters  the  shadow,  a  portion  of  her  sur- 
face seems  to  be  cut  off  and  to  disappear  entirely,  and  her  vis- 
ible portion  continually  grows  smaller,  until,  in  case  of  a  total 
eclipse,  her  whole  disk  is  immei-sed  in  the  shadow.  When  this 
occui-s,  it  is  found  that  she  is  not  entirely  invisible,  but  still 
faintly  shines  with  a  lurid  copper-coloi'ed  light.  This  light  is 
refracted  into  the  shadow  by  the  earth's  atmosphere,  and  its 
amount  may  be  greater  or  less,  according  to  the  quantity  of 
clouds  and  vapor  in  the  atmosphere  around  that  belt  of  the 
earth  which  the  sunlight  must  graze  in  order  to  reach  the  moon. 

In  about  half  of  the  lunar  eclipses,  the  moon  passes  so  far 
above  or  below  the  centre  of  the  shadow  that  part  of  her  body 
is  in  it,  and  part  outside,  at  the  time  of  greatest  eclipse.  This 
is  called  ^partial  €clij)se  of  the  moon.  The  magnitude  of  a 
partial  eclipse,  whetlier  of  the  sun  or  moon,  was  measured  by 
the  older  astronomers  in  digits.  The  diameter  of  the  solar  or 
lunar  disk  was  divided  into  twelve  equal  parts,  called  digits; 
and  the  magnitude  of  the  eclipse  was  said  to  be  equal  to  the 
number  of  digits  cut  off  by  the  shadow  of  the  earth  in  case  of 
a  lunar  eclipse,  or  by  the  moon  in  case  of  a  solar  eclipse.  The 
most  ancient  astronomei's  were  in  the  habit  of  measuring  the 
digits  by  surface :  when  the  moon  was  said  to  be  eclipsed  four 
digits,  it  meant  that  one -third  of  her  surface,  and  not  one- 
third  her  diameter,  was  eclipsed. 

The  duration  of  an  eclipse  varies  between  veiy  wide  limits, 
according  to  whether  it  is  nearly  central  or  the  contrary.  The 
duration  of  a  solar  eclipse  depends  upon  the  time  required  for 
the  moon  to  pass  over  the  distance  from  where  she  first  comes 
into  apparent  contact  with  the  sun's  disk,  until  she  separates 
from  it  again ;  and  this,  in  the  case  of  eclipses  which  are  pret- 
ty large,  may  range  between  two  and  three  hours.  In  a  total 
eclipse,  however,  the  apparent  disk  of  the  moon  exceeds  that 


ECLIPSES  OF  THE  SUN  AND  MOON.  29 

of  the  Sim  by  so  small  an  amount,  that  it  takes  her  but  a  short 
time  to  pass  far  enough  to  uncover  some  part  of  the  sun's 
disk;  the  time  is  rarely  more  than  live  or  six  minutes,  and 
sometimes  only  a  few  seconds.  A  total  eclipse  of  the  moon 
ma}',  however,  last  nearly  two  hours,  and  the  partial  eclipses 
on  each  side  of  the  total  one  may  extend  the  whole  duration 
of  the  eclipse  to  three  or  four  hours. 

Total  eclipses  of  the  sun  afford  veiw  rare  and  highly  prized 
opportunities  for  studying  the  operations  going  on  around  that 
luminary.     Of  these  we  shall  speak  in  a  subsequent  chapter. 

Keturning,  now,  to  the  apparent  motions  of  the  sun  and 
moon  around  the  celestial  sphere,  we  see  that  since  the  moon's 
orbit  has  two  opposite  nodeB  in  which  it  crosses  the  ecliptic, 
and  the  sun  passes  through  the  entire  course  of  the  ecliptic  in 
the  course  of  the  yeai-,  it  follows  that  there  are  two  periods  in 
the  course  of  a  year  during  which  the  sun  is  near  a  node,  and 
eclipses  may  occur.  Roughly  speaking,  these  periods  are  each 
about  a  month  in  duration,  and  we  may  call  them  seasons  of 
eclipses.  For  instance,  it  will  be  seen  on  Map  Y,  that  the 
sun  passes  one  node  of  the  moon's  orbit  towards  the  end  of 
February,  1877.  A  season  of  eclipses  for  that  year  is  there- 
fore February  and  the  first  half  of  March.  Actually,  there  is 
a  total  eclipse  of  the  moon  on  February  27th,  and  a  very  small 
eclipse  of  the  sun  on  March  14:th,  of  that  year,  visible  only  in 
Northern  Asia.*  From  tins  time,  the  sun  is  so  far  from  the 
node  that  there  can  be  no  eclipses  until  he  approaches  the 
other  node  in  August.  Then  we  have  the  two  eclipses  of  the 
sun  already  mentioned,  and,  between  them,  a  total  eclipse  of 
the  moon  on  August  23d.  Thus,  in  the  year  1877,  the  fii'st 
season  of  eclipses  is  in  February  and  March,  and  the  second 
in  August  and  September. 

We  have  said  that  the  length  of  each  eclipse  season  is  about 
a  month.  To  speak  with  greater  accuracy,  the  average  season 
for  eclipses  of  the  sun  extends  18  days  before  and  after  the 

*  There  is  an  extraoidinary  coincidence  between  this  eclipse  and  that  of  Au- 
gust 8th  of  the  same  year,  both  being  visible  from  nearly  the  same  region  in  Ce>i- 
tral  Siberia. 


30       SYSTEM  OF  TEE  WORLD  HISTORICALLY  DEVELOPED- 

sun's  passage  through  the  node,  while  that  for  lunar  eclipses 
extends  11|^  days  on  each  side  of  the  node.  The  total  season 
is,  therefore,  36  days  for  solar,  and  23  days  for  lunar  eclipses. 

Owing  to  the  constant  motion  of  the  moon's  node  already 
described,  the  season  of  eclipses  will  not  be  the  same  from 
year  to  year,  but  will  occur,  on  the  average,  about  20  days 
earlier  each  year.  We  have  seen  that  the  sun  passed  tlie  de- 
scending node  of  the  moon  marked  on  Map  III.  on  August 
24th,  1877;  but  during  the  year  following  the  node  will  have 
moved  so  far  to  the  west  that  the  sun  will  again  reach  it  on 
August  5th,  1878.  The  effect  of  this  constant  shifting  of  tlie 
nodes  and  seasons  of  eclipses  is  that  in  1887  the  August  sea- 
son will  be  shifted  back  to  February,  and  tlie  February  season 
to  August.  The  reader  who  wishes  to  find  the  middle  of  the 
eclipse  seasons  for  twenty  or  thirty  years  can  do  so  by  starting 
from  March  1st  and  August  24th,  1877,  and  subtracting  19f 
days  for  each  subsequent  year. 

There  is  a  relation  between  the  motions  of  the  sun  and 
moon  which  materially  assisted  the  early  astronomers  in  the 
prediction  of  eclipses.  We  have  said  that  the  moon  makes 
one  revolution  among  the  stars  in  about  27^  days.  Since  the 
node  of  the  orbit  is  constantly  moving  back  to  meet  the  moon, 
as  it  were,  she  will  return  to  her  node  in  a  little  less  than  this 
period — namely,  as  shown  by  modern  observations,  in  a  mean 
interval  of  27.21222  days.  The  sun,  after  passing  any  node 
of  the  orbit,  will  reach  the  same  node  again  in  3-46.G201  days. 
The  relation  between  these  numbers  is  this :  242  returns  of 
the  moon  to  a  node  take  very  nearly*  the  same  time  with  19 
returns  of  the  sun,  the  intervals  being 

2i2  returns  of  the  moon  to  her  node 6585.357  days; 

19       "         "      sun  to  moon's  node 6585.780    " 

Consequently,  if  at  any  time  the  sun  and  moon  should  start 
out  together  from  a  node,  they  would,  at  the  end  of  6585 
days,  or  18  years  and  11  days,  be  again  found  together  very 
near  the  same  node.  During  the  interval,  there  would  have 
been  223  new  and  full  moons,  but  none  so  near  the  node  as 


ECLIPSES  OF  THE  SUN  AND  MOON.  31 

this.  The  exact  time  required  for  223  lunations  is  6585.3212 
days;  so  that,  in  the  case  supposed,  the  223d  conjunction  of 
the  sun  and  moop  would  happen  a  little  before  they  reached 
the  node,  their  distance  from  it  being,  by  calculation,  a  little 
less  than  one  of  their  diameters,  or,  more  exactly,  28'.  If, 
instead  of  being  exactly  at  the  node,  they  are  any  given  dis- 
tance from  it,  say  3°  east  or  west,  then,  in  the  same  period, 
they  will  be  again  together  within  half  a  degree  of  the  same 
distance  from  the  node. 

The  period  just  found  was  called  the  Saros,  p,nd  may  be  ap- 
plied in  this  way :  Let  us  note  the  exact  time  of  the  middle 
of  any  eclipse,  either  of  the  moon  or  of  the  sun ;  then  let  us 
oount  forwards  6585  c^ays,  7  hours,  42  minutes,  and  we  shall 
find  another  eclipse  of  very  nearly  the  same  kind.  Reduced 
to  years,  the  interval  will  be  18  years  and  10  or  11  days,  ac- 
cording to  whether  the  29th  of  February  has  intervened  four 
or  five  times  during  the  interval.  This  being  true  of  every 
eclipse,  if  we  record  all  the  eclipses  which  occur  during  a 
period  of  18  years,  we  shall  find  the  same  series  after  10  or 
11  days  to  begin  over  again  ;  but  the  new  series  will  not  gen- 
erally be  visible  at  the  same  places  with  the  old  ones,  or,  at 
least,  will  not  occur  at  the  same  time  of  day,  since  the  mid- 
dle will  be  nearly  eight  hours  later.  Not  till  the  end  of  three 
periods  will  they  recur  near  the  same  meridian ;  and  then, 
owing  to  the  period  not  being  exact,  the  eclipse  will  not  be 
precisely  of  the  same  magnitude,  and,  indeed,  may  fail  entire- 
ly. Every  successive  recurrence  of  an  eclipse  at  the  end  of 
the  period  being  28'  farther  back  relatively  to  the  node,  the 
conjunction  must,  in  process  of  time,  be  so  far  back  from  the 
node  as  not  to  produce  an  eclipse  at  all.  During  nearly  every 
period  it  M'ill  be  found  that  some  eclipse  fails,  and  that  some 
new  one  enters  in.  A  new  eclipse  of  the  moon  thus  entering 
will  be  a  very  small  one  indeed.  At  every  successive  recur- 
rence of  its  period  it  will  be  larger,  until,  about  its  thirteenth 
recurrence,  it  will  be  total.  It  will  be  total  for  about  twenty- 
two  or  twenty-three  recurrences,  when  it  will  become  partial 
ou'?e  more,  but  on  the  opposite  side  of  the  moon  from  that  on 


32       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

which  it  was  fii-st  seen.  There  will  tlien  be  about  thirteen  par- 
tial eclipses,  each  smaller  than  the  last,  until  they  fail  entirely. 
The  whole  interval  of  time  over  which  the  recurrence  of  a 
lunar  eclipse  thus  extends  will  be  about  48  periods,  or  86o-J 
years.  The  solar  eclipses,  occurring  farther  from  the  node, 
will  last  yet  longer,  namely,  from  65  to  70  periods,  or  over 
1200  years. 

As  a  recent  example  of  the  Saros,  we  may  cite  some  total 
eclipses  of  the  sun  well  known  in  recent  times ;  for  instance, 

1842,  July  Sth,  l*"  8  a.m.,  total  eclipse,  observed  in  Europe ; 
■  1860,  July  18th,  Q*"  a.m.,  total  eclipse  America  and  Spain ; 
1878,  July  29th,  i*"  2  p.m.,  one  visible  in  Colorado  and  on  the  Pacific  Coast. 

A  yet  more  remarkable  series  of  total  eclipses  of  the  sun 
occui-s  in  the  years  1S50, 1S6S,  18S6,  etc.,  the  dates  being — 

1850,  August  7th,  •i*'  4  p.m.,  in  the  Pacific  Ocean ; 

1868,  Angnst  17th,  12''  p.m.,  in  India; 

1886,  August  29th,  S*"  a.m.,  in  the  Central  Atlantic  Ocean  and  Southern  Africa; 

1904,  September  9th,  noon,  in  South  America. 

This  series  is  remarkable  for  the  long  duration  of  totality, 
amounting  to  some  six  minutes. 

It  must  be  undei-stood  that  the  various  numbers  we  have 
given  in  this  section  are  not  accurate  for  all  cases,  because  the 
motions  both  of  the  sun  and  moon  are  subject  to  certain  small 
irregularities  which  may  alter  the  times  of  eclipses  by  an  hour 
or  more.  "We  have  given  only  mean  values,  which  are,  how- 
ever, always  quite  near  the  truth. 

§  7,  The  Ptolemaic  System. 

There  is  still  extant  a  work  which  for  fourteen  centuries 
was  a  sort  of  astronomical  Bible,  from  which  nothing  was 
taken,  and  to  which  nothing  material  in  principle  was  added. 
This  is  the  "Almagest"  of  Ptolemy,  composed  about  the  mid- 
dle of  the  second  century  of  our  era.  Xearly  all  we  know  of 
the  ancient  astronomy  as  a  science  is  derived  from  it.  Frag- 
ments of  other  ancient  authors  have  come  down  to  us,  and 
most  of  the  ancient  writei*s  make  occasional  allusions  to  astro- 
nomical phenomena  or  theories,  from  which  various  ideas  re- 


THE  PTOLEMAIC  SYSTEM.  33 

specting  the  ancient  astronomy  have  been  gleaned;  but  the 
work  of  Ptolemy  is  the  only  complete  compendium  which  we 
possess.  Although  his  system  is  in  several  important  points 
erroneous,  it  yet  represents  the  salient  features  of  the  apparent 
motions  of  the  heavenly  bodies  witli  entire  accuracy.  Defec- 
tive as  it  is  when  measured  by  our  standard,  it  is  a  marvel  of 
ingenuity  and  research  when  measured  by  the  standard  of  the 
times. 

The  immediate  object  of  the  present  chapter  is  to  explain 
the  apparent  movements  of  the  planets,  which  can  be  most 
easily  done  on  the  Ptolemaic  system.  But,  on  account  of  its 
historic  interest,  we  shall  begin  with  a  brief  sketch  of  the 
propositions  on  which  the  system  rests,  giving  also  Ptolemy's 
method  of  proving  them.  His  fundamental  doctrines  are  that 
tiie  heavens  are  spherical  in  form,  and  all  the  heavenly  mo- 
tions  spherical  or  in  circles ;  that  the  earth  is  also  spherical, 
and  situated  in  the  centre  of  the  heavens,  or  celestial  sphere, 
where  it  remains  quiescent,  and  that  it  is  in  magnitude  only  a 
point  when  compared  with  the  sphere  of  the  stars.  We  shall 
give  Ptolemy's  views  of  these  propositions,  and  his  attempts 
to  prove  them,  in  their  regular  order. 

1st.  The  Heavenly  Bodies  move  in  Circles. — Here  Ptole- 
my refers  principally  to  the  diurnal  motion,  whereby  every 
heavenly  body  is  apparently  carried  around  the  earth,  or,  rath- 
er, around  the  pole  of  the  heavens,  in  a  circle  every  day.  But 
all  the  ancient  and  mediaeval  astronomers  down  to  the  time 
of  Kepler  had  a  notion  that,  the  circle  being  the  most  perfect 
plane  figure,  all  the  celestial  motions  must  take  place  in  cir- 
cles; and  as  it  was  found  that  the  motions  were  never  nni- 
form,  they  supposed  these  circles  not  to  be  centred  on  the 
earth.  Where  a  single  circle  did  not  suffice  to  account  for 
the  motion,  they  introduced  a  combination  of  circular  motions 
in  a  manner  to  be  described  presently. 

2d.  The  Earth  is  a  Sphere.  —  That  the  earth  is  rounded 
from  east  to  west  Ptolemy  proves  by  the  fact  that  the  sun, 
moon,  and  stars  do  not  rise  and  set  at  the  same  moment  to  all 
the  inhabitants  of  the  earth.     The  times  at  which  eclipses  of 


34       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

the  moon  are  seen  in  different  countries  being  compared,  it  is 
found  that  the  farther  tlie  observer  is  west,  the  earher  is  the 
hour  after  sunset.  As  the  time  is  really  the  same  everywhere, 
this  shows  that  the  sun  sets  later  the  farther  we  go  to  the  west. 
Again,  if  the  earth  were  not  rounded  from  north  to  south,  a 
star  passing  the  meridian  in  the  north  or  south  horizon  would 
always  pass  in  the  horizon,  however  far  to  the  north  or  south 
the  observer  might  travel.  But  it  is  found  that  when  an  ob- 
server travels  towards  the  south,  the  stars  in  the  north  ap- 
proach the  horizon,  and  the  circles  of  their  diurnal  motion  cut 
below  it,  while  new  stars  rise  into  view  above  the  south  hori- 
zon. This  shows  that  the  horizon  itself  changes  its  direction 
as  the  observer  moves.  Finally,  from  whatever  direction  we 
approach  elevated  objects  from  the  sea,  we  see  that  their  bases 
are  first  hidden  from  view  by  the  curvature  of  the  water,  and 
gradually  rise  into  view  as  we  approach  them. 

3d,  The  Earth  is  in  the  Centre  of  the  Celestial  Sphere. — 
If  the  earth  were  displaced  from  the  centre,  there  would  be 
various  irregularities  in  the  apparent  daily  motion  of  the  ce- 
lestial sphere,  the  stars  appearing  to  move  faster  on  the  side 
towards  which  the  earth  was  situated.  If  it  were  displaced 
towards  the  east,  we  should  be  nearer  the  heavenly  bodies 
when  they  are  rising  than  when  they  are  setting,  and  they 
would  appear  to  move  more  rapidly  in  the  east  than  in  the 
west.  The  forenoons  would  therefore  be  shorter  than  the  af- 
ternoons. Towards  whatever  side  of  the  turning  sphere  it 
might  be  moved,  tlie  heavenly  bodies  would  seem  to  move 
more  rapidly  on  that  side  than  on  the  other.  No  such  irreg- 
ularity being  seen,  but  the  diurnal  motion  taking  place  with 
perfect  uniformity,  the  earth  must  be  in  the  centre  of  mo- 
tion. 

4th.  The  Earth  has  no  Motion  of  Translation  —  Because 
if  it  had  it  would  move  away  from  the  centre  towards  one 
side  of  the  celestial  sphere,  and  the  diurnal  revolution  of  the 
stars  would  cease  to  be  uniform  in  all  its  parts.  But  the  uni- 
formity of  motion  just  described  being  seen  from  year  to  year, 
the  earth  must  preserve  its  position  in  the  centre  of  the  sphere. 


THE  PTOLEMAIC  SYSTEM.  35 

It  will  be  interesting  to  analyze  these  propositions  of  Ptole- 
my, to  see  what  is  true  and  what  is  false.  The  first  proposi- 
tion—  that  the  heavenly  bodies  move  in  circles,  or,  as  it  is 
more  literally  expressed,  that  the  heavens  move  spherically — 
is  quite  true,  so  far  as  the  apparent  diurnal  motion  is  con- 
cerned. What  Ptolemy  did  not  know  was  that  this  motion  is 
only  apparent,  arising  from  a  rotation  of  the  earth  itself  on  its 
axis.  The  se(;ond  proposition  is  perfectly  correct,  and  Ptole- 
my's proofs  that  the  earth  is  round  are  those  still  found  in  our 
school-books  at  the  end  of  seventeen  hundred  years.  Most 
curious,  however,  is  the  mixture  of  truth  and  falsehood  in  the 
third  and  fourth  propositions,  that  the  earth  remains  quies- 
cent. We  cannot  denounce  it  as  unqualiiiedly  false,  because, 
in  a  certain  sense,  and  indeed  in  the  only  sense  in  which  there 
is  any  celestial  sphere,  the  eai-th  may  be  said  to  remain  in  the 
centre  of  the  sphere.  What  Ptolemy  did  not  see  is  that  this 
sphere  is  only  an  ideal  one,  which  the  spectator  carries  with 
him  wherever  he  goes.  His  demonstration  that  the  centre  of 
revolution  of  the  sphere  is  in  the  earth  is,  in  a  certain  sense, 
correct ;  but  what  he  i-eally  proves  is  that  the  earth  revolves 
on  its  own  axis.  He  did  not  see  that  if  the  earth  could  carry 
the  axis  of  revolution  witli  it,  his  demonstration  of  the  quies- 
cence of  the  earth  WDuld  fall  to  the  ground. 

Considerable  insight  into  Ptolemy's  views  is  gained  by  his 
answers  to  two  objections  against  his  system.  The  first  is  the 
vulgar  and  natural  one,  that  it  is  paradoxical  to  suppose  that 
a  body  like  the  earth  could  remain  supported  on  nothing,  and 
still  be  at  rest.  These  ol)jectors,  he  says,  reason  froin  what 
they  see  happen  to  small  bodies  around  them,  and  not  from 
what  is  proper  to  tlie  universe  at  large.  There  is  neither  up 
nor  down  in  the  celestial  spaces,  for  we  cannot  conceive  of  it 
in  a  sphere.  What  we  call  down  is  simply  the  direction  of 
our  feet  towards  the  centre  of  the  earth,  the  direction  in 
which  heavy  bodies  tend  to  fall.  The  earth  itself  is  but  a 
point  in  comparison  with  the  celestial  spaces,  and  is  kept  fixed 
by  the  forces  exerted  upon  it  on  all  sides  by  the  universe, 
which  is  infinitely  larger  than  it,  and  similar  in  all  its  parts. 


36       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

•  This  idea  is  as  near  an  approach  to  that  of  universal  gravita- 
tion as  the  science  of  tlie  times  would  admit  of. 

He  then  says  there  are  othei-s  who,  admitting  this  reason- 
ing, pretend  that  nothing  hinders  ns  from  supposing  that  the 
heavens  are  immovable,  and  that  the  earth  itself  turns  round 
its  own  axis  once  a  day  from  west  to  east.  It  is  certainly 
singular  that  one  who  had  risen  so  far  above  the  ilhisions  of 
sense  as  to  demonstrate  to  tlie  world  that  the  eaith  was  round ; 
that  up  and  down  were  only  relative;  and  that  heavy  bodies 
fell  towards  a  centre,  and  not  in  some  unchangeable  direction, 
should  not  have  seen  the  correctness  of  this  view. 

T(J  refute  the  doctrine  of  the  earth's  rotation,  he  proceeds 
in  a  way  the  opposite  of  that  whicli  he  took  to  refute  those 
who  thought  the  earth  could  not  rest  on  nothing.  He  said  of 
the  latter  that  they  regarded  solely  what  was  around  them  on 
the  earth,  and  did  not  consider  what  was  proper  to  the  uni- 
verse at  large.  To  those  who  maintained  the  earth's  rotation, 
he  says,  if  we  consider  only  the  movements  of  the  stars,  tliere 
is  nothing  to  oppose  tlieir  doctrine,  which  he  admits  has  the 
merit  of  simplicity ;  but  in  view  of  what  passes  around  us  and 
in  the  air,  their  doctrine  is  ridiculous.  He  then  entere  into  a 
disquisition  on  the  relative  motion  of  light  and  heavy  bodies, 
which  is  extremely  obscure;  but  his  conclusion  is  that  if  the 
earth  really  rotated  with  the  enormous  velocity  necessary  to 
(;arry  it  round  in  a  day,  the  air  would  be  left  behind.  If  they 
say  that  the  earth  carries  round  the  air  with  it,  he  replies  that 
this  could  not  be  true  of  bodies  floating  in  the  air;  and  hence 
concludes  that  the  doctrine  of  the  eartli's  rotation  is  not  tena- 
ble. It  is  clear,  from  this  argument,  that  if  Ptolemy  and  his 
contemporaries  had  devoted  to  experimental  physics  half  the 
careful  observation,  research,  and  reasoning  which  we  find  in 
their  astronomical  studies,  they  could  not  have  failed  to  estab- 
lish the  doctrine  of  the  earth's  rotation. 

In  the  Ptolemaic  system,  all  the  celestial  motions  are  repre- 
sented by  a  series  of  circular  motions.  "We  have  already  ex- 
plained the  motions  of  the  sun  and  moon  among  the  stars,  the 
first  describing  a  complete  circuit  of  the  heavens  from  west  to 


THE  PTOLEMAIC  SYSTEM.  87 

east  in  a  year,  and  the  second  a  similar  circuit  in  a  month. 
Though  not  entirely  uniform,  these  movements  are  always  for- 
ward. But  it  is  not  so  with  the  five  planets  —  Mercury,  Ve- 
nus, Mars,  Jupiter,  and  Saturn.  These  move  sometimes  to  the 
east  and  sometimes  to  the  west,  and  are  sometimes  stationary.* 
On  the  whole,  however,  the  easterly  movements  predominate; 
and  the  planets  really  oscillate  around  a  certain  mean  point 
itself  in  regular  motion  towards  the  east.  Let  us  take,  for  in- 
stance, the  planet  Jupiter.  Suppose  a  certain  fictitious  Jupi- 
ter performing  a  circuit  of  the  heavens  among  the  stars  every 
twelve  years  with  a  regular  easterly  motion,  just  as  the  sun 
performs  such  a  circuit  every  year;  then  the  I'eal  Jupiter  will 
be  found  to  oscillate,  like  a  pendulum,  on  each  side  of  the  fic- 
titious planet,  but  never  swinging  more  than  12°  from  it.  The 
time  of  each  double  oscillation  is  about  thirteen  months — that 
is,  if  on  January  1st  we  find  it  passing  the  fictitious  planet 
towards  the  west,  it  will  continue  its  westerly  swing  about 
three  months,  when  it  will  gradually  stop,  and  return  with  a 
somewhat  slower  motion  to  the  fictitious  planet  again,  passing 
to  the  east  of  it  the  middle  of  July.  The  easterly  swing  will 
continue  till  about  the  end  of  October,  when  it  will  return 
towards  the  west.  The  westerly  or  backward  motion  is  called 
retTograde^  and  the  easterly  motion  direct.  Between  the  two 
is  a  point  at  which  the  planet  appears  stationary  once  more. 
The  westerly  motions  are  called  retrograde  because  they  are 
in  the  opposite  direction  both  to  the  motion  of  the  sun  among 
the  stars,  and  to  the  average  direction  in  which  all  the  planets 
move.  It  was  seen  by  Hipparchus,  who  lived  three  centuries 
before  Ptolemy,  that  this  oscillating  motion  could  be  repre- 
sented by  supposing  the  real  Jupiter  to  describe  a  circular  or- 
bit around  the  fictitious  Jupiter  once  in  a  year.  This  orbit  is 
called  the  epicycle,  and  thus  we  have  the  celebrated  epicyclic 
theory  of  the  planetary  motions  laid  down  in  the  "  Almagest." 
The  movement  of  the  planet  on  this  theory  can  be  seen  by 

*  It  may  not  be  amiss  to  remind  the  reader  once  more  that  we  here  leave  the 
diurnal  motion  of  the  stars  entirely  out  of  sight,  and  consider  only  the  motions  of 
the  planets  relative  to  the  stars. 


38       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

Fig.  10.  E  is  tlie  earth,  around  winch  the  fictitious  Jupiter 
moves  in  the  dotted  circle,  1, 2,  3, 4,  etc.  To  form  the  epicycle 
in  which  the  real  planet  moves,  we  must  suppose  an  arm  to  be 
constantly  turning  round  the  fictitious  planet  once  a  year,  on 
the  end  of  which  Jupiter  is  carried.  This  arm  will  then  be  in 
the  successive  positions,  1 1',  2  2',  3  3',  etc.,  represented  by  the 
light  dotted  lines.  Drawing  a  line  through  the  successive  po- 
sitions 1',  2',  3',  etc.,  of  the  real  Jupiter,  we  shall  have  a  series 
of  loops  representing  its  apparent  orbit. 


■esfr 


/ 


/ 

I 

I 
I 
I 

; 


[ 
\ 

/ 

/ 

/ 

/ 

o^ 


Fig.  10.— Showing  the  apparent  orbit  of  a  planet,  regarding  the  earth  as  at  rest. 

It  will  be  seen  that  although  it  requires  only  a  year  for  the 
arm  carrying  the  real  Jupiter  to  perform  a  complete  revolu- 
tion and  return  to  its  primitive  direction,  it  requires  about 
thirteen  months  to  form  a  complete  loop,  because,  owing  to 
the  motion  of  the  fictitious  planet  in  its  orbit,  the  arm  must 
move  more  than  a  complete  revolution  to  finish  the  loop.  For 
instance,  referring  again  to  Fig.  10,  comparing  the  positions 
11'  and  8  8',  it  will  be  seen  that  the  arm,  being  in  the  same 
direction,  has  performed  a  complete  revolution ;  but,  owing  to 
the  curvature  of  the  orbit,  it  does  not  reach  the  middle  of  the 
second  loop  imtil  it  attains  the  position  9  0'. 


TEE  PTOLEMAIC  SYSTEM. 


39 


The  planets  of  which  the  radius  of  the  epicycle  makes  an 
annual  revolution  in  this  way  are  Mars,  Jupiter,  and  Saturn, 
The  complete  apparent  orbits  of  the  last  two  planets  are  shown 
in  the  next  figure,  taken  from  Arago.  By  the  radius  of  the 
epicj'^cle  we  mean  the  imaginary  revolving  arm  which,  turn- 
ing round  the  fictitious  planet,  carries  the  real  planet  at  its 


Fig.  11.— Apparent  orbits  of  Jupiter  and  Saturn,  1708-1737,  after  Caseiui. 

end.  The  law  of  revolution  of  this  arm  is,  that  whenever  the 
planet  is  opposite  the  sun,  the  arm  points  towards  the  earth, 
as  in  the  positions  11',  9  9',  in  which  cases  the  sun  will  be  on 
the  side  of  the  earth  opposite  the  planet ;  while,  whenever  the 
planet  is  in  conjunction  with  the  sun,  the  arm  points  from  the 
earth.  This  fact  was  well  known  to  the  ancient  astronomers, 
and  their  calculations  of  the  motions  of  the  planets  were  all 


40       SYSTEM  OF  THE  WOELD  HISTORICALLY  DEVELOPED. 

founded  upon  it;  but  they  do  not  seem  to  have  noticed  the 
very  important  corollary  from  it,  that  the  direction  of  the 
radius  of  the  epicycle  of  Mars,  Jupiter,  and  Saturn  is  alwaj's 
the  same  with  that  of  the  sun  from  the  earth.  Had  they 
done  so,  they  could  hardly  have  failed  to  see  that  the  epicycles 
could  be  abolished  entirely  by  supposing  that  it  was  the  earth 
which  moved  round  the  sun,  and  not  the  sun  round  the  earth. 
The  peculiarity  of  the  planets  Mercury  and  Yenus  is  that 
tlie  fictitious  centres  around  which  they  oscillate  are  always  in 
the  direction  of  the  sun,  or,  as  we  now  know,  the  sun  himself 
is  the  centre  of  their  motions.  They  are  never  seen  more  than 
a  limited  distance  from  that  luminary,  Venus  oscillating  about 
45°  on  each  side  of  the  sun,  and  Mercury  from  16°  to  29°.  It 
is  said  that  the  ancient  Egyptians  really  did  make  the  sun  the 
centre  of  the  motion  of  these  two  planets ;  and  it  is  difficult  to 
see  how  any  one  could  have  failed  to  do  so  after  learning  the 
laws  of  their  oscillation.  Yet  Ptolemy  rejected  this  system, 
placing  their  orbits  between  the  earth  and  sun  without  assign- 
ing any  good  reason  for  the  course. 

The  arrangement  of  the  planets  on  the  Ptolemaic  system  is 
shown  in  Fig.  12.  The  nearest  planet  is  the  moon,  of  which 
the  ancient  astronomers  actually  succeeded  in  roughly  meas- 
uring the  distance.  The  remaining  planets  are  arranged  in 
the  same  order  with  their  real  distance  from  the  sun,  except 
that  the  latter  takes  the  place  assigned  to  the  earth  in  the 
modern  system.     Thus  Ave  have  the  following  order : 

Tiie  Moon, 

Mercury, 

Yenus, 

The  Sun, 

Mars, 

Ju})iter, 

Saturn. 
Outside  of  Saturn  was  the  sphere  of  the  fixed  stars. 

This  order  of  the  planets  nuist  have  been  a  matter  of  opin- 
ion rather  than  of  demonstration,  it  being  correctly  judged 
by  the  ancient  astronomers  that  those  which  seemed  to  move 


THE  PTOLEMAIC  SYSTEM. 

Saturn 


41 


Fig.  12.— Arrangement  of  the  seven  planets  iu  the  Ptolemaic  system.  The  orbits,  .is 
marked,  are  those  of  the  fictitious  planets,  the  real  planets  beiuj;  supposed  to  describe 
a  series  of  loops. 

more  slowly  were  the  more  distant.  This  system  inade  it 
quite  certain  that  the  moon  was  tlie  nearest  planet,  and  Mars, 
Jupiter,  and  Saturn,  in  their  order,  the  most  distant  ones.  But 
the  relative  positions  of  the  Sun,  Mercury,  and  Venus  were 
more  in  doubt,  since  they  all  performed  a  revolution  round 
the  celestial  sphere  in  a  year.  So,  while  Ptolemy,  as  we  have 
just  said,  placed  Mercui-y  and  Yenns  between  the  earth  and 
the  sun,  Plato  placed  them  beyond  the  sun,  the  order  being, 
Moon,  Sun,  Mercury,  Venus,  Mars,  Jupiter,  Saturn. 

Hipparchus  and  Ptolemy  made  a  series  of  investigations  re- 
specting the  times  of  revolution  of  the  planets,  and  the  inequal- 
ities of  their  motions,  of  which  it  is  worth  while  to  give  a  brief 


i2       SYSTEM  OF  THE  WORLD  HISTORICALLY  BEVELOrED. 


summary.  The  former  was  no  doubt  an  abler  astronomer  than 
Ptolemy;  but  as  he  was,  so  far  as  we  know,  the  first  accurate 
observer  of  the  celestial  motions,  he  could  not  make  a  suf- 
ficiently long  series  of  observations  to  determine  all  the  peri- 
ods of  the  planets.  Ptolemy  had  the  advantage  of  being  able 
to  combine  his  own  observations  with  those  of  llipparchus, 
three  centuries  earlier. 

Imperfect  though  their  means  of  observation  were,  these 
observers  found  that  the  easterly  movements  of  the  planets 
among  the  stare  were  none  of  them  uniform.  This  held  true 
not  only  of  the  sun  and  moon,  but  of  the  fictitious  planets 

already  described.  Hence  they 
invented  the  eccentric,  and  sup- 
posed the  motions  to  be  really  cii- 
cular  and  uniform,  but  in  circles 
not  centred  in  the  earth.  In  Fig. 
13,  let  E  be  the  earth,  and  C  the 
centre  around  which  the  planet 
really  revolves.  Then,  when  the 
planet  is  passing  the  point  P^ 
which  is  nearest  the  earth,  its  an- 
gular motion  would  seem  more 
rapid  than  the  average,  because 
in  cjeneral  the  anjjular  velocity 
of  a  moving  body  is  greater  the 
nearer  the  observer  is  to  it,  while 
when  passing  A  it  will  seem  to  be 
more  slow  than  the  averasre.  The  anovular  velocitv  being 
always  greatest  in  one  point  of  the  orbit,  and  least  in  a  point 
directly  opposite,  changing  regularly  from  the  maximum  to 
the  minimum,  the  general  features  of  the  movement  are  cor 
rectly  represented  by  the  eccentric.  By  comparing  the  angu- 
lar velocities  in  different  points  of  the  orbit,  Hipparchus  and 
Ptolemy  were  able  to  determine  the  supposed  distance  of  the 
earth  from  the  centre,  or  rather  the  proportion  of  this  distance 
to  the  distance  of  the  planet.  The  distance  thus  determined 
is  double  its  true  amount.     The  point  P  is  called  the  Perigee, 


Pig.  13.  — The  eccentria  Shows  how 
the  ancients  represented  the  unequal 
apparent  velocities  of  the  planets 
when  their  real  motion  was  supposed 
uniform,  by  placing  the  earth  away 
from  the  centre  of  motion,  at  E. 


TEE  PTOLEMAIC  SYSTEM.  43 

and  A  the  Apogee.  The  distance  CE  from  tlie  earth  to  the 
centre  of  motion  is  the  eccentricity.  As  there  was  no  way  of 
determining  the  absolute  dimensions  of  the  orbit,  it  was  neces- 
sary to  take  the  ratio  of  CE  to  the  radius  of  the  orbit  CP  or 
CE  iov  the  eccentricity.* 

In  determining  the  motions  of  the  moon,  Hipparchus  and 
Ptolemy  depended  almost  entirely  on  observations  of  lunar 
eclipses.  The  first  of  these,  it  is  said,  was  observed  at  Babylon 
in  the  first  year  of  Mardocempad,  between  the  29th  and  30th 
days  of  the  Egyptian  month  Thoth.  It  commenced  a  little 
more  than  an  hour  after  the  moon  rose,  and  was  total.  The 
date,  in  our  reckoning,  was  b.c.  720,  Marcli  19th.  The  series 
of  eclipses  extended  from  tliis  date  to  that  of  Ptolemy  him- 
self, who  lived  between  eight  apd  nine  centuries  later.  If  the 
observations  of  these  eclipses  had  been  a  little  more  precise, 
they  would  still  be  of  great  value  to  us  in  fixing  the  mean 
motion  of  the  moon.  As  it  is,  we  can  now  calculate  tlie  cir- 
cumstances of  an  ancient  eclipse  from  our  modern  tables  of 
the  sun  and  moon  almost  as  accurately  as  any  of  the  ancient 
astronomers  could  observe  it. 

Notwithstanding  the  extremely  imperfect  character  of  the 
observations,  both  Hipparchus  and  Ptolemy  made  discoveries 
respecting  the  peculiarities  of  the  moon's  motions  which  show 
a  most  surprising  depth  of  researcli.  By  comparing  tlie  inter- 
vals between  eclipses,  they  found  that  her  motion  was  not  uni- 
form, but  that,  like  the  sun,  she  moved  faster  in  some  parts  of 
her  orbit  than  in  others.  To  account  for  this,  they  supposed 
her  orbit  eccentric,  like  that  of  the  sun;  that  is,  the  earth,  in- 
stead of  being  in  the  centre  of  the  circular  orbit  of  the  moon, 
was  supposed  to  be  displaced  by  about  a  tenth  part  the  whole 
distance  of  that  body.  So  far  the  orbit  of  the  moon  was  like 
that  of  the  sun  and  the  fictitious  planets,  except  that  its  eccen- 
tricity was  greater.     But  a  long  series  of  observations  sliowed 

*  Compared  with  the  modern  theory  of  the  elliptic  motion,  approximately  treat- 
ed, the  distance  CE  is  double  the  eccentricity  of  the  ellipse.  One-half  the  appar- 
ent inequality  is  really  caused  by  the  orbit  being  at  various  distances  from  the 
earth  or  sun,  but  the  other  half  is  real. 


44       SYSTEM  OF  THE  WORLD  HISTOBICALLT  DEVELOPED. 

that  the  perigee  and  apogee  did  not,  as  in  the  case  of  the  sun 
and  planets,  remain  in  the  same  points  of  the  orbit,  but  moved 
forwards  at  sucli  a  rate  as  to  carry  them  round  the  heavens  in 
nine  years ;  that  is,  supposing  Fig.  13  to  represent  the  orbit  of 
the  moon,  tlie  centre  of  the  circle  C  revolved  round  the  earth 
in  nine  years,  and  the  orbit  changed  its  position  accordingly. 

It  was  also  found  by  Ptolemy,  by  measuring  the  apparent 
angle  between  the  moon  and  sun  in  various  points  of  the 
orbit  of  the  former,  that  there  was  yet  another  inequality  in 
her  motion.  This  has  received  the  name  of  the  evection.  In 
consequence  of  this  inequality,  the  moon  oscillates  more  than 
a  degree  on  each  side  of  her  position  as  calculated  from  the 
eccentric,  in  a  period  not  differing  much  from  her  revolution 
round  the  earth.  To  represent  this  motion,  Ptolemy  had  to 
introduce  a  small  additional  epicycle,  as  in  the  case  of  the 
planets,  only  the  radius  was  so  small  that  there  was  no  looping 
of  the  orbit.  In  consequence,  his  theory  of  the  moon's  motion 
was  quite  complicated ;  yet  he  managed  to  represent  this  mo- 
tion, within  the  limits  of  the  erroi^s  of  his  observations,  by  a 
combination  of  circular  motions,  and  thus  saved  the  favorite 
theoiy  of  the  times,  that  all  the  celestial  motions  were  circular 
and  uniform, 

§  8.  The  Calendar. 

One  of  the  earliest  purposes  of  the  study  of  the  celestial 
motions  was  that  of  finding  a  convenient  measurement  of 
time.  This  application  of  astronomy,  being  of  great  antiquity, 
having  been  transmitted  to  us  without  any  fundamental  altera- 
tion, and  depending  on  the  apparent  motions  of  the  sun  and 
moon,  which  we  have  studied  in  this  chapter,  is  naturally  con- 
sidered in  connection  with  the  ancient  astronomy. 

The  astronomical  divisions  of  time  are  the  day,  the  month, 
and  the  year.  The  week  is  not  such  a  division,  because  it  does 
not  correspond  to  any  astronomical  cycle,  although,  as  we  shall 
presently  see,  a  certain  astronomical  signification  was  said  to 
have  been  given  to  it  by  the  ancient  astrologers.  Of  these 
divisions  the  day  is  the  most  well-marked  and  striking  through 


THE  CALENDAB.  45 

out  the  habitable  portion  of  the  globe.  Had  a  people  lived  at 
or  near  the  poles,  it  would  have  been  less  striking  than  the  year. 
But  wherever  man  existed,  there  was  a  regular  alternation  of 
day  and  night,  with  a  corresponding  alternation  in  his  physical 
condition,  both  occurring  with  such  regularity  and  uniformity 
as  to  furnish  in  all  ages  the  most  definite  unit  of  time.  For 
merely  chronological  purposes  the  day  would  have  been  the 
only  unit  of  time  tlieoretically  necessary;  for  if  mankind  had 
begun  at  some  early  age  to  number  every  day  by  counting 
from  1  forwards  without  limit,  and  had  every  historical  event- 
been  recorded  in  connection  with  the  number  of  the  day  on 
which  it  happened,  there  would  have  been  far  less  uncertain- 
ty about  dates  than  now  exists.  But  keeping  count  of  such 
large  numbers  as  would  have  accumulated  in  the  lapse  of  cen- 
turies would  have  been  very  inconvenient,  and  a  simple  count 
of  time  by  days  has  never  been  used  for  the  purposes  of  civil 
life  through  any  greater  period  than  a  single  month. 

Next  to  the  day,  the  most  definite  and  striking  division  of 
time  is  the  year.  The  natural  year  is  that  measured  by  the 
retui-n  of  tlie  seasons.  All  the  operations  of  agriculture  are 
so  intimately  dependent  on  this  recurrence,  that  man  must 
have  begun  to  make  use  of  it  for  measuring  time  long  before 
he  had  fully  studied  the  astronomical  cause  on  which  it  de- 
pends. The  years  in  the  lifetime  of  any  one  generation  not 
being  too  numerous  to  be  easily  reckoned,  the  year  was  found 
to  answer  every  purpose  of  measuring  long  intervals  of  time. 

The  number  of  days  in  tlie  year  is,  however,  too  great  to 
be  conveniently  kept  count  of;  an  intermediate  measure  was 
therefore  necessary.  This  was  suggested  by  the  motion  and 
phases  of  the  moon.  The  "  new  moon  "  being  seen  to  emerge 
from  the  sun's  rays  at  intervals  of  about  30  days,  a  measure 
of  very  convenient  length  was  found,  to  which  a  permanent 
interest  was  attachc-ij  by  the  religious  rites  connected  with  the 
reappearance  of  the  moon. 

The  week  is  a  division  of  time  entirely  disconnected  with 
the  month  and  year,  the  employment  of  which  dates  from  the 
Mosaic  dispensation.     The  old  astrologers  divided  the  seven 


46    SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

days  of  the  week  among  the  seven  planets,  not  in  the  order  of 
their  distance  from  the  sun,  but  in  one  shown  by  the  follow- 
ing figure.  If  we  go  round  the  circle  in  the  direction  oppo- 
site that  of  the  hands  of  a  watch,  we  shall  find  the  names  of 
the  seven  planets  of  the  ancient  astronomy  in  their  supposed 
order;*  while, if  we  follow  the  lines  drawn  in  the  circle  from 
side  to  side,  we  shall  have  the  days  of  the  week  in  their  order. 


^^eflo 


':^^ 


Fig.  U.— Showing  the  astrological  division  of  the  seven  planets  among  the  days  or  the 

week. 

If  the  lunar  month  had  been  an  exact  number  of  days,  say 
30,  and  the  year  an  exact  number  of  months,  as  12,  there 
would  have  been  no  difficulty  in  the  use  of  these  cycles  for 
the  measurement  of  time.  But  the  former  is  several  hours 
less  than  30  days,  while  the  latter  is  nearly  12^  lunar  months. 
In  the  attempt  to  combine  these  measures,  the  ancient  calen- 


*  See  pages  40,  41. 


THE  CALENDAR.  47 

dars  were  thrown  into  a  confusion  which  made  them  very  per- 
plexing, and  which  we  see  to  this  day  in  the  irregular  lengths 
of  our  months.  To  describe  all  the  devices  which  we  know  to 
have  been  used  for  remedying  these  difficulties  w^ould  be  very 
tedious ;  we  shall  therefore  confine  ourselves  to  their  general 
nature. 

The  lunar  month,  or  the  mean  interval  between  successive 
new  moons,  is  very  nearly  29^  days.  In  counting  months  by 
the  moon,  it  was  therefore  common  to  make  their  length  29 
and  30  days,  alternately.  But  the  period  of  29^  days  is  really 
about  three-quarters  of  an  hour  too  short.  In  the  course  of 
three  years  the  count  will  therefore  be  a  day  in  error,  and  it 
will  be  necessary  to  add  a  day  to  one  of  the  months.  When 
lunar  months  were  used,  the  year,  comprising  12  such  months, 
would  consist  of  only  354  days,  and  would  therefore  be  11 
days  too  short.  Nevertheless,  such  a  year  was  used  both  by 
the  Greeks  and  Romans,  and  is  still  used  by  the  Mahome- 
tans; the  Romans,  however,  in  the  calendar  of  Numa,  adding 
22  or  23  days  to  every  alternate  year  by  inserting  the  inter- 
calary month  Mercedonius  between  the  23d  and  24th  of  Feb- 
ruary. 

The  irregularity  and  inconvenience  of  reckoning  by  lunar 
months  caused  them  to  be  very  generally  abandoned,  the  only 
reason  for  their  retention  being  religious  observances  due  at 
the  time  of  new  moon,  which,  among  the  Jews  and  otlier  an- 
cient nations,  were  regarded  as  of  the  highest  importance.  Ac- 
cordingly, we  find  the  Egyptians  counting  by  months  of  30 
days  each,  and  making  every  year  consist  of  12  such  months 
and  five  additional  days,  making  365  days  in  all.  As  the  true 
length  of  the  year  was  known  to  be  about  six  hours  greater 
than  this,  the  equinox  would  occur  six  hours  later  every  year, 
and  a  raontli  later  after  the  lapse  of  120  years.  After  the  lapse 
of  1460  years,  according  to  the  calculations  of  the  time,  each 
season  would  have  made  a  complete  course  through  the  twelve 
months,  and  would  then  have  returned  once  more  at  the  same 
time  of  year  as  in  the  beginning.  This  was  termed  the  Sothic 
Period;  but  the  error  of  each  year  being  estimated  a  little 

5 


4S        SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

too  great,  as  we  now  know,  the  true  length  of  the  period 
would  have  been  about  1500  yeai-s. 

The  confusion  in  the  Greek  year  was  partly  remedied 
through  the  discovery  by  Meton  of  the  cycle  which  has  since 
borne  his  name.  This  cycle  consists  of  19  solar  years,  during 
which  the  moon  changes  235  times.  The  error  of  this  cycle 
is  very  small,  as  may  be  seen  from  the  following  periods,  com- 
puted from  modern  data : 

Days.       Hoars.     Min. 

235  lunations  require  in  the  mean 6939       16      31 

19  true  solar  years  (tropical) 6939       14       27 

19  Julian  years  of  365^  days ; G939       18        0 

Hence,  if  we  take  235  lunar  months,  and  divide  them  up  as 
nearly  evenly  as  is  convenient  into  19  years,  the  mean  length 
of  these  yeai*s  will  be  near  enough  right  for  all  the  purposes 
of  civil  reckoning.  The  yeai-s  of  each  cycle  were  numbered 
from  1  to  19,  and  the  number  of  the  year  was  called  the  Gold- 
en Kumber,  from  its  having  been  ordered  to  be  inscribed  on 
the  monuments  in  letters  of  gold. 

This  is  the  only  religious  festival  which,  in  Christian  coun- 
tries,  depends  directly  on  the  motion  of  the  moon.  The  rule 
for  determining  Easter  is  that  it  is  the  Sunday  following  the 
first  full  moon  which  occurs  on  or  after  the  21st  of  March. 
The  dates  of  the  full  moon  correspond  to  the  Metonic  Cycle ; 
that  is,  after  the  lapse  of  19  years  they  recur  on  or  about  the 
same  day  of  the  year.  Consequently,  if  we  make  a  list  of  the 
dates  on  which  the  Paschal  full  moon  occurs,  we  shall  find 
no  two  dates  to  be  the  same  for  nineteen  successive  years; 
but  the  twentieth  will  occur  on  the  same  day  with  the  fii"st, 
or,  at  most,  only  one  day  different,  and  then  the  whole  series 
will  be  repeated.  Consequently,  the  Golden  Number  for  the 
year  shows,  with  sufiicient  exactness  for  ecclesiastical  purposes, 
on  what  day,  or  how  many  days  after  the  equinox,  the  Paschal 
full  moon  occui*s.  The  church  calculations  of  Easter  Sunday 
are,  however,  founded  upon  very  old  tables  of  the  moon,  so 
that  if  we  fixed  it  by  the  actual  moon,  we  should  often  find 
the  calendar  feast  a  week  in  error. 


THE  CALENDAR.  49 

The  basis  of  the  calendars  now  employed  throughout  Chris 
tendom  was  laid  by  Julius  Csesar.  Previous  to  his  time,  the 
Roman  calendar  was  in  a  state  of  great  confusion,  the  nomi- 
nal length  of  the  year  depending  veiy  largely  on  the  caprice 
of  the  ruler  for  the  time  being.  It  was,  however,  very  well 
known  that  the  real  length  of  the  solar  year  was  about  365i 
days ;  and,  in  order  that  the  calendar  year  might  have  the  same 
mean  length,  it  was  prescribed  that  the  ordinary  year  should 
consist  of  365  days,  but  that  one  day  should  be  added  to  every 
fourth  year.  The  lengths  of  the  months,  as  we  now  have  them, 
were  finall}'  arranged  by  the  immediate  successors  of  Caesar. 

The  Julian  calendar  continued  unaltered  for  about  sixteen 
centuries ;  and  if  the  true  length  of  the  tropical  year  had  been 
365^  days,  it  would  have  been  in  use  still.  But,  as  we  have 
seen,  this  period  is  about  11^  minutes  longer  than  the  solar 
year,  a  quantity  which,  repeated  every  year,  amounts  to  an  en- 
tire day  in  128  years.  Consequently,  in  the  sixteenth  century, 
the  equinoxes  occurred  11  or  12  days  sooner  than  they  should 
have  occurred  according  to  the  calendar,  or  on  the  lOtli  in- 
stead of  the  21st  of  March.  To  restore  them  to  their  original 
position  in  the  year,  or,  more  exactly,  to  their  position  at  the 
time  of  the  Council  of  Nice,  was  the  object  of  the  Gregorian 
reformation  of  the  calendar,  so  called  after  Pope  Gregory 
XIII.,  by  whom  it  was  directed.  The  change  consisted  of 
two  parts : 

1.  The  5th  of  October,  1582,  according  to  the  Julian  calen- 
dar, was  called  the  15th,  the  count  being  thus  advanced  10 
days,  and  the  equinoxes  made  once  more  to  occur  about  March 
21st  and  September  21st. 

2.  The  closing  year  of  each  century,  1600,  1700,  etc.,  in- 
stead of  being  each  a  leap-year,  as  in  the  Julian  calendar, 
should  be  such  only  when  the  number  of  the  century  was  di- 
visible by  4.  While  1600,  2000,  2400,  etc.,  were  to  be  leap- 
years,  as  before,  1700,  1800,  1900,  2100,  etc.,  were  to  be  re- 
duced to  365  days  each. 

This  change  in  the  calendar  was  soon  adopted  by  the  Catho- 
lic countries,  and^  more  slowly,  by  Protestant  ones — England, 


50     system:  of  tee  wobld  eistoeically  developed. 

among  the  latter,  holding  out  for  more  than  a  century,  but 
finally  entering  into  the  change  in  1752.  In  Russia  it  was 
never  adopted  at  all,  the  Julian  calendar  being  still  continued 
in  that  country.  Consequently,  the  Russian  reckoning  is  now 
12  days  behind  ours,  the  10  days'  difference  during  the  six- 
teenth and  seventeenth  centui'ies  being  increased  by  the  days 
dropped  from  the  yeai-s  1700  and  ISOO  in  the  new  reckoning. 

The  length  of  the  mean  Gregorian  year  is  365'^  5^  49"»  12'; 
while  that  of  the  tropical  year,  according  to  the  best  astn>nom- 
ical  determination,  is  365"^  5^  48™  46^  The  former  is,  there- 
fore, still  26  seconds  too  long,  an  error  whicli  will  not  amount 
to  an  entire  day  for  more  than  3000  veal's.  If  there  were 
any  object  in  having  the  calendar  and  the  astronomical  yeare 
in  exact  coincidence,  the  Gi-egorian  year  would  be  accurate 
enough  for  all  practical  purposes  during  many  centuries.  In 
fact,  however,  it  is  difficult  to  show  what  practical  object  is  to 
be  attained  by  seeking  for  any  such  coincidence.  It  is  im- 
portant that  summer  and  winter,  seed-time  and  harvest,  shall 
occur  at  the  same  time  of  the  year  through  several  successive 
generations ;  but  it  is  not  of  the  slightest  importance  that 
they  should  occur  at  the  same  time  now  that  they  did  5000 
years  ago,  nor  would  it  cause  any  difficulty  to  our  descendants 
of  5000  years  hence  if  the  equinox  should  occur  in  the  middle 
of  February,  as  would  be  the  case  should  the  Julian  calendar 
have  been  continued. 

The  change  of  calendar  met  with  much  popular  opposition, 
and  it  may  hercafter  be  conceded  that  in  this  instance  the 
common  sense  of  the  people  was  more  nearly  right  than  the 
wisdom  of  the  learned.  An  additional  complication  was  in- 
troduced into  the  reckoning  of  time  without  any  other  real 
object  than  that  of  making  Easter  come  at  the  right  time. 
As  the  end  of  the  century  approaches,  the  question  of  making 
1900  a  leap-year,  as  usual,  M-ill  no  doubt  be  discussed,  and  it  is 
possible  that  some  concerted  action  may  be  taken  on  the  part  of 
leadins:  nations  looking  to  a  return  to  the  old  mode  of  reckoning. 


COPERNICUS.  61 


CHAPTER  11. 

THE   COPEKNICAN    SYSTEM,  OR   THE   TKUE    MOTIONS   OF   THE    HEAV- 
ENLY  BODIES. 

§  1.  Copernicus. 

In  the  first  section  of  the  preceding  chapter  we  described 
the  apparent  diurnal  motion  of  the  lieavens,  wliorehy  all  the 
lieavenly  bodies  appear  to  be  carried  round  in  circles,  thus 
performing  a  revolution  every  day.  Any  observer  of  this  mo- 
tion who  should  suppose  tlie  earth  to  be  flat,  and  the  dii-ection 
we  call  downwai'd  everywhere  the  same,  would  necessarily  re- 
gard it  as  real.  A  very  little  knowledge  of  geometry  would, 
however,  show  him  that  the  appearance  might  be  accounted 
for  by  supposing  the  earth  to  revolve.  The  seemingly  fatal 
objection  against  this  view  wonld  be  that,  if  such  were  the 
case,  the  surface  of  the  earth  could  not  remain  level,  and  ev- 
ery thing  would  slide  away  from  its  position.  But  it  was  im- 
possible for  men  to  navigate  the  ocean  without  perceiving  the 
rotnndity  of  its  surface,  and  we  have  no  record  of  a  time  when 
it  was  not  known  that  the  earth  was  round.  We  have  seen 
that  Ptolemy  not  only  was  acquainted  with  the  true  figure  of 
the  earth,  but  knew  that  in  magnitude  it  was  so  mnch  smaller 
than  the  celestial  spaces,  or  sphere  of  the  heavens,  as  to  be  only 
a  point  in  comparison.  He  had,  therefore,  all  the  knowledge 
necessary  to  enable  him  to  see  that  the  moving  body  was  much 
more  likely  to  be  the  earth  than  to  be  the  sphere  of  the  heav- 
ens. Nevertheless,  he  rejected  the  theory  on  obscure  physical 
grounds,  as  shown  in  the  last  chapter,  the  nntenability  of  which 
would  have  been  proved  him  by  a  few  very  simple  physical  ex- 
periments. And  although  it  is  known  that  the  doctrine  of  the 
earth's  motion  was  sustained  by  others  in  his  age,  notably  by 
Timocharis,  yet  the  weight  of  his  authority  was  so  great  as 


52       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

not  only  to  override  all  their  arguments,  but  to  carry  his  views 
through  fourteen  centuries  of  the  intellectual  history  of  man. 

The  history  of  astronomy  during  these  centuries  ofifei-s  hard- 
ly anything  of  interest  to  the  general  reader.  There  was  no 
telescope  to  explore  the  heavens,  and  no  genius  arose  of  suffi- 
cient force  to  unravel  the  maze  of  their  mechanism.  It  was 
mainly  through  the  Arabs  that  any  systematic  knowledge  of 
the  science  was  preserved  for  the  use  of  posterity.  The  as- 
tronomers of  this  people  invented  improved  methods  of  ob- 
serving the  positions  of  the  heavenly  bodies,  and  were  thus 
able  to  make  improved  tables  of  their  motions.  They  meas- 
ured the  obliquity  of  the  ecliptic,  and  calculated  eclipses  of 
the  sun  and  moon  with  greater  precision  than  the  ancient 
Greeks  could  do.  The  predictions  of  the  science  thus  gradu- 
ally increased  in  accuracy,  but  no  positive  step  was  taken  in 
the  direction  of  discovering  the  true  nature  of  the  apparent 
movements  of  the  heavens. 

The  honor  of  first  proving  to  the  world  what  the  true  theory 
of  the  celestial  motions  is  belongs  almost  exclusively  to  Coper- 
nicus. It  is  true  that  we  have  some  reason  to  believe  tliat 
Pythagoras  taught, that  the  sun,  and  not  the  earth,  was  the 
centre  of  motion,  and  that  he  was,  therefore,  the  tii"st  to  solve 
the  great  problem.  Bat  he  did  not  teach  this  doctrine  public- 
ly, and  the  very  vague  statements  of  his  private  teachings  on 
this  point  which  have  been  handed  down  to  us  are  so  mixed 
up  with  the  speculations  which  the  Greek  philosopher  com- 
bined with  their  views  of  nature,  that  it  is  hard  to  say  with 
precision  whether  Pythagoras  had  or  had  not  fully  seized  the 
truth.  It  is  certain  that  no  modern  would  receive  the  credit 
of  any  discovery  without  giving  more  convincing  proofs  of  the 
correctness  of  his  views  than  we  have  any  reason  to  suppose 
that  Pythagoras  gave  to  his  disciples. 

The  great  merit  of  Copernicus,  and  the  basis  of  his  claim  to 
the  discovery  in  question,  is  that  he  was  not  satisfied  with  a 
mere  statement  of  his  views,  but  devoted  a  large  part  of  the 
labor  of  a  life  to  their  demonstration,  and  thus  placed  them  in 
such  a  light  as  to  render  their  ultimate  acceptance  inevitable. 


COPERNICUS.  53 

Apart  from  all  questions  of  the  truth  or  falsity  of  his  theory, 
the  great  work  in  which  it  was  developed,  "Z^e  Revolutionibus 
Orhiuin  CodestiwnV  would  deservedly  rank  as  the  most  im- 
portant compendium  of  astronomy  which  had  appeared  since 
Ptolemy.  Few  books  have  been  more  completely  the  labor  of 
a  lifetime  than  this.  Copernicus  was  born  at  Thorn,  in  Prus- 
sia, in  1473,  twenty  years  before  the  discovery  of  America, 
but  studied  at  the  University  of  Cracow.  He  became  an  ec- 
clesiastical dignitary,  holding  the  rank  of  canon  during  a  large 
portion  of  his  life,  and  finding  ample  leisure  in  this  position 
to  pui'sue  his  favorite  studies.  He  is  said  to  have  conceived  of 
the  true  system  of  the  world  as  early  as  1507.  He  devoted  the 
years  of  his  middle  life  to  the  observations  and  computations 
necessary  to  the  pei'fection  of  his  system,  and  communicated 
his  views  to  a  few  friends,  but  long  refused  to  publish  tliem, 
fearing  the  popular  prejudice  which  might  thus  be  excited. 
In  1540,  a  brief  statement  of  them  was  published  by  his  friend 
Rheticus ;  and,  as  this  was  favorably  received,  he  soon  con- 
sented to  the  publication  of  his  great  work.  The  first  printed 
copy  was  placed  in  his  hands  only  a  few  hours  before  his 
death,  which  occurred  in  May,  1543. 

The  fundamental  principles  of  the  Copernican  system  are 
embodied  in  two  distinct  propositions,  which  have  to  be  proved 
separately,  and  one  of  which  might  have  been  true  without 
the  other  being  so.     The}'  are  as  follows : 

1.  The  diurnal  revolution  of  the  heavens  is  only  an  appar- 
ent motion,  caused  by  a  diurnal  revolution  of  the  earth  on  an 
axis  passing  through  its  centre. 

2.  The  earth  is  one  of  the  planets,  all  of  which  revolve 
round  the  sun  as  the  centre  of  motion.  The  true  centre  of 
the  celestial  motions  is  therefore  not  the  earth,  but  the  sun. 
For  this  reason  the  Copernican  system  is  frequently  spoken  of 
in  historical  discussions  as  the  "heliocentric  theory." 

The  first  proposition  is  the  one  with  the  proof  of  which  Co- 
pernicus begins.  He  explains  how  an  apparent  motion  may 
result  from  a  real  motion  of  the  person  seeing,  as  M'ell  as  from 
a  motion  of  the  object  seen,  and  thus  shows  that  the  diurnal 


54       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

motion  may  be  aoeountcd  for  just  as  well  by  a  revolution  of 
tlie  eartli  as  by  one  of  tbe  heavens.  To  sailors  on  a  ship  sail- 
ing on  a  smooth  sea,  the  ship,  and  every  thing  in  it,  seems  to  be 
at  rest  and  the  shore  to  be  in  motion.  Which,  then,  is  more 
likely  to  be  in  motion,  the  earth  or  the  whole  universe  outside 
of  it?  In  whatever  jjroportion  the  heavens  are  greater  than 
the  earth,  in  the  same  proportion  must  their  motion  be  more 
rapid  to  carry  them  round  in  twenty -four  hours.  Ptolemy 
himself  shows  that  the  heavens  were  so  immense  that  the 
earth  was  but  a  point  in  comparison,  and,  for  any  thing  that 
is  known,  they  may  extend  into  infinity.  Then  we  should  re- 
quire an  inlinite  velocity  of  revolution.  Therefore,  it  is  far 
more  likely  that  it  is  this  comparative  point  that  turns,  and 
that  the  iinivei'se  is  fixed,  than  the  reverse. 

The  second  principle  of  the  Copernican  system — that  the 
apparent  annual  motion  of  the  sun  among  the  stars,  described 
in  §  3  of  the  preceding  chapter,  is  really  due  to  an  annual  revo- 
lution of  the  earth  around  the  sun — rests  upon  a  \evy  beautiful 
result  of  the  laws  of  relative  motion.  This  movement  of  the 
earth  explains  not  only  this  apparent  revolution  of  the  sun, 
but  the  apparent  epicyclic  motion  of  the  planets  described  in 
treating  of  the  Ptolemaic  system. 

In  Fig.  15,  let  S  represent  the  &\m,ABCD  the  orbit  of  the 
earth  around  it,  and  the  figures  1,  2,  3,  4,  5, 6,  six  successive 
positions  of  the  earth.  These  positions  would  be  about  two 
weeks  apart.  Also,  let  EFGIl  represent  the  apparent  sphere 
of  the  fixed  stars.  Then,  an  observer  at  1,  viewing  the  sun  in 
the  direction  1^,  will  see  him  as  if  he  were  in  the  celestial 
sphere  at  the  point  1',  because,  having  no  conception  of  the 
actual  distance,  the  sun  will  appear  to  him  as  if  actually  among 
the  stars  at  \'  which  lie  in  the  same  straiglit  line  witli  him. 
Wlien  the  earth,  with  the  observer  on  it,  reaches  2,  he  will  see 
the  sun  in  the  direction  2/iS2',  that  is,  as  if  among  the  stars  in 
2'.  That  is,  during  the  two  weeks'  interval,  the  sun  will  ap- 
parently have  moved  among  the  stars  by  an  angle  equal  to  the 
actual  angular  ntotion  of  the  earth  around  the  sun.  So,  as  the 
earth  passes  through  the  successive  positions  3,  4,  5,  6,  the  sun 


COPERNICUS. 


55 


will  appear  in  the  positions  3',  4',  5',  6',  and  the  motion  of  the 
earth  continuing  all  the  way  round  its  orbit,  the  sun  will  ap- 
pear to  move  through  the  entire  circle  EFGII.  Thus  we 
have,  as  a  result  of  the  annual  motion  of  the  earth  around  the 
sun,  the  annual  motion  of  the  sun  around  the  celestial  sphere 
already  described  in  the  third  section  of  the  preceding  chapter. 


Fig.  15 — Apparent  annual  motion  of  the  sun  explained. 

Let  us  now  see  how  this  same  motion  abolishes  tlie  compli- 
cated system  of  epicycles  by  which  the  ancient  astronomers 
represented  the  planetary  motions.  A  theorem  on  wliich  this 
explanation  rests  is  this :  If  an  observer  in  unconscious  mo- 
tion sees  an  ohject  at  rest,  that  object  will  seem  to  him  to  be 
m,oving  in  a  direction  opposite  to  his  oion,  and  xoith  an  equal 
velocity.  A  familiar  instance  of  this  is  the  apparent  motion 
D 


56       SYSTEM  OF  THE  WOBLD  HISTORICALLY  DEVELOPED, 


,- A 


of  objects  on  shore  to  passengers  on  a  steamer.  In  Fig.  16, 
let  us  suppose  an  observer  on  the  earth  carried  around  the 

sun  .S'in  the  orbit  ABCDEF, 
but  imagining  himself  at  rest 
in  the  centre  of  motion  8.  Su})- 
pose  that  he  observes  tlie  ap- 
parent motion  of  the  planet  P^ 
which  is  really  at  rest.  How 
will  the  planet  appear  to  move  ? 
To  show  this,  we  represent  ap- 
parent directions  and  motions 
by  dotted  lines.  Let  us  begin 
with  the  observer  at  A^  from 
which  position  he  really  sees 
the  planet  in  the  direction  and 
distance  AP.  But,  imagining 
himself  at  <S',  he  thinks  he  sees 
the  planet  at  the  point  «,  the 
distance  and  direction  of  which 
Sa  is  the  same  with  AP.  As 
he  passes  unconsciously  from  A 
to  B^  the  planet  seems  to  him  to 
move  past  from  a  to  J  in  the  op- 
posite direction ;  and,  still  think- 
ing himself  at  rest  in  /S,  he  sees 
the  planet  in  i,  the  line  Sb  be- 

FiG.  16.-Showin-  how  the  npparent  epi-   J,^^  Qn\X2X  and  parallel   tO  BP. 
cyclic  motion  of  the  planets  is  accounted     .,  t         e 

for  by  the  motion  of  the  earth  round  the   As    he    rCCcdcS    from   tllC    plaU- 

^""-  et  through  the  arc  BCD,  the 

planet  seems  to  recede  from  him  through  hcd.  While  lie 
moves  from  left  to  right  through  DE,  the  planet  seems  to 
move  from  right  to  left  through  de.  Finally,  as  he  approaches 
the  planet  through  the  arc  EFA^  the  planet  will  seem  to  ap- 
proach him  through  efa,  and  when  he  gets  back  to  A  he 
will  locate  the  planet  at  a,  as  in  the  beginning.  Thus,  in 
consequence  of  the  motion  of  the  observer  around  the  circle 
ABCDEF  tlif  planet,  though  really  at  rest,  will  seem  to  him 


COPEBNICUS.  57 

I, 

to  move  through  a  corresponding  circle,  ahcdef.  If  there  are 
a  number  of  planets,  they  will  all  seem  to  describe  correspond- 
ing circles  of  the  same  magnitude. 

If  the  planet  P,  instead  of  being  at  rest,  is  in  motion,  the 
apparent  circular  motion  will  be  combined  with  the  forward 
motion  of  the  planet,  and  the  latter  will  now  describe  a  circle 
around  a  centre  which  is  in  motion.  Thus  we  have  the  appar- 
ent motion  of  the  planets  around  a  moving  centre,  as  already 
described  in  the  Ptolemaic  system.  We  have  said,  in  §  7  of 
the  preceding  chapter,  that  by  this  system  the  motions  of  the 
planets  are  represented  by  supposing  a  fictitious  planet  to  re- 
volve around  the  heavens  with  a  regular  motion,  while  the 
real  planet  revolves  around  this  fictitious  one  as  a  centre  once 
a  year.  Here,  the  progressive  inotion  of  the  fictitious  planet 
is  {i7i  the  case  of  the  outer  j^lctnets  Mars,  Jupiter,  and  Sat- 
urn) the  motion  of  the  real  planet  around  the  sun,  while  the 
circle  which  the  real  planet  describes  around  this  moving  cen- 
tre is  only  an  apparent  motion  due  to  the  observer  being  car- 
ried around  the  sun  on  the  earth.  If  the  reader  will  com- 
pare the  epicyclic  motion  of  Ptolemy,  represented  in  Figs.  10 
and  11  with  the  motion  explained  in  Fig.  16,  he  will  find  that 
they  correspond  in  every  paiticular.  In  the  case  of  the  inner 
planets,  Mercury  and  Yenus,  which  never  recede  far  from  the 
sun,  the  epicyclic  motion  by  which  they  seem  to  vibrate  from 
one  side  of  the  sun  to  the  other  is  due  to  their  orbital  motion 
around  the  sun,  while  the  progressive  motion  with  which  they 
follow  the  sun  is  due  to  the  revolution  of  the  earth  around 
the  sun. 

We  may  now  see  clearly  how  the  retrograde  motion  and 
stationary  phases  of  the  planets  are  explained  on  the  Coper- 
nican  system.  The  earth  and  all  the  planets  are  really  mov- 
ing round  the  sun  in  a  direction  which  we  call  east  on  the 
celestial  sphere.  When  the  earth  and  an  outer  planet  are 
on  the  same  side  of  the  sun,  they  are  moving  in  the  same 
direction ;  but  the  earth  is  moving  faster  than  the  planet. 
Hence,  to  an  observer  on  the  earth,  the  planet  seems  to  be 
moving  west,  though  its  real  motion  is  east.     As  the  earth 


58        HYSTEM  OF  THE   WORLD  HISTORICALLY  DEVELOPED. 

passes  to  the  opposite  side  of  the  snn  from  the  planet,  it 
changes  its  motion  to  a  direction  tlie  opposite  of  tliat  of  the 
planet,  and  thus  the  westerly  motion  of  the  latter  appears  to 
be  increased  by  the  whole  motion  of  the  earth.*  Between 
these  two  motions  there  is  a  point  at  which  the  planet  does 
not  seem  to  move  at  all.  This  is  called  the  stationary  point. 
If  the  planet  we  consider  is  not  an  outer,  but  an  inner  one, 
Mercury  or  Yenus,  and  we  view  it  when  between  us  and  the 
sun,  its  motion  to  us  is  reversed,  because  Me  see  it  fioni  the 
side  opposite  the  sun.  Hence  it  seems  to  move  west  to  us, 
and  it  is  retrosrrade.  The  earth  is  indeed  moving:  in  the  same 
real  direction;  but  since  the  planet  moves  faster  than  the 
earth,  its  retrograde  motion  seems  to  predominate.  As  the 
planet  passes  round  in  its  orbit,  it  fii"st  appeal's  stationary, 
and  then,  passing  to  the  opposite  side  of  the  sun,  it  seems 
direct. 

Let  us  now  dwell  for  a  moment  on  some  considerations 
which  will  enable  us  to  do  justice  to  the  Ptolemaic  system,  as 
it  is  called,  by  seeing  how  necessary  a  step  it  was  in  the  evo- 
lution of  the  true  theory  of  the  universe.  The  great  merit  of 
that  system  consisted  in  the  analysis  of  the  seemingly  compli- 
cated motions  of  the  planets  into  a  combination  of  two  circular 
motions,  the  one  that  of  a  fictitious  planet  around  the  celestial 
sphere,  the  other  that  of  the  real  planet  around  the  fictitious 
one.  Without  that  separation,  the  constant  oscillations  of  the 
planets  back  and  forth  could  not  have  suggested  any  idea 
whatever,  except  that  of  a  motion  too  complicated  to  be  ex- 
plained on  mechanical  principles.  But  when,  leaving  out  of 
sight  the  regular  forward  motion  of  the  mean  or  fictitious 
planet,  the  attention  was  directed  to  the  epicyclic  motion 
alone,  one  could  not  fail  to  see  the  remarkable  correspondence 
between  this  latter  motion  and  the  apparent  annual  motion 
of  the  sun.     Seeing  this,  it  took  a  very  small  step  to  see  that 

*  It  must  not  be  forgotten  that  the  direction  east  in  the  heavens  is  a  cur\-ed  di^ 
rection,  as  it  were,  and  is  opposite  on  opposite  sides  of  the  sun  or  celestial  sphere. 
For  instance,  the  motions  of  the  stars  as  they  rise  and  as  they  set  are  opposite, 
but  both  are  considered  west. 


COPERNICUS.  59 

the  snn,  and  not  tlie  earth,  was  the  centre  of  planetary  motion. 
Then  nothing  but  the  ilhisioiis  of  sense  remained  to  prevent 
the  acceptance  of  the  theory  tliat  the  earth  was  itself  a  planet 
moving  roimd  the  sun,  and  that  both  the  annual  motion  of  the 
sun  and  the  epicyclic  motion  of  the  planets  were  not  real,  but 
apparent  motions,  due  to  the  motion  of  the  earth  itself;  and 
in  no  other  way  than  this  could  the  heliocentric  theory  have 
been  developed. 

The  Copernican  system  affords  the  means  of  determining 
the  proportions  of  the  solar  system,  or  the  relative  distances  of 
the  several  planets,  with  great  accuracy.  That  is,  if  we  take 
as  our  measuring -rod  the  distance  of  the  earth  from  the  sun, 
we  can  determine  how  many  lengths  of  this  rod,  or  what  frac- 
tional parts  of  its  length,  will  give  the  distance  of  each  planet, 
although  the  length  of  the  rod  itself  may  remain  unknown. 
This  determination  rests  on  the  principle  that  the  apparent 
circle  or  epicycle  described  by  the  planet  in  Fig.  16  is  of  the 
same  magnitude  with  the  actual  orbit  described  by  the  earth 
around  the  sun.  Hence,  the  nearer  the  observer  is  to  this  cir- 
cle, the  larger  it  will  appear.  The  apparent  epicycle  described 
by  Neptune  is  i-ather  less  than  two  degrees  in  radius ;  that  is, 
the  true  planet  Neptune  is  seen  to  swing  a  little  less  than  two 
degrees  on  each  side  of  its  mean  position  in  consequence  of 
the  annual  motion  of  the  earth  round  the  snn.  This  shows 
that  the  orbit  of  the  earth,  as  seen  from  Neptune,  subtends  an 
angle  of  only  two  degrees.  On  the  other  hand,  the  planet 
Mars  generally  swings  more  than  40°  on  each  side;  sometimes, 
indeed,  more  than  45°.  From  this  a  trigonometrical  calcula- 
tion shows  that  its  mean  distance  is  only  about  half  as  much 
again  as  that  of  the  earth ;  and  the  fact  that  the  apparent 
swing  is  variable  shows  the  distance  to  be  different  at  different 
times. 

As  it  will  be  of  interest  to  see  how  nearly  Copernicus  was 
able  to  determine  the  distances  of  the  planets,  M-e  present  his 
results  in  the  following  table,  together  with  what  we  now 
know  to  be  the  true  numbers.  The  numbei*s  given  are  deci- 
mal fractions,  expressing  the  least  and  greatest  distance  of 


60       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

each  planet  from  the  sun,  the  distance  of  the  earth  being  taken 
as  unity.* 


Planets. 

Least  Dista>-ce.                    Geeatest  Di6ta>-ce. 

Copemicns. 

Modern,      il  Copemicns. 

Modem. 

Mercuiy 

Venus 

Mars 

Jupiter 

Saturn 

0.326 
0.709 
1.373 
4.980 
8.66 

0.308 
0.718       1 
1.382 
4.952 
9.00         1 

0.405 
0.730 
1.666 
5.453 
9.76 

0.467 
0.728 
1.666 
5.454 
10.07 

Considering  the  extremely  imperfect  means  of  observation 
which  the  times  afforded,  these  results  of  Copernicus  come 
very  near  the  truth.  The  greatest  proportional  deviation  is  in 
the  case  of  Mercury,  the  most  difficult  of  all  the  planets  to 
observe,  even  to  the  present  day.  It  is  said  that  Copernicus 
died  without  ever  seeing  this  planet. 

The  eccentricities  of  the  orbits  were  represented  by  Coper- 
nicus in  a  way  which  agrees  exactly  with  the  modern  formulae 
when  only  a  rough  approximation  is  sought  for.  Like  Ptole- 
my, he  supposed  the  orbits  o^  the  planets  not  to  be  centred  on 
the  sun,  but  to  be  displaced  by  a  small  quantity  termed  the 
eccentincity.  But  it  had  long  been  known  that  the  theory  of 
uniform  motion  in  an  eccentric  circle,  though  it  might  make 
the  irregularities  in  the  planet's  angular  motion  come  out  all 
right,  would  make  the  changes  of  distance  double  their  true 
value.  He  therefore  took  for  the  eccentricity  a  mean  between 
that  which  would  satisfy  the  motion  in  longitude,  and  that 
which  would  give  the  changes  of  distance,  and  added  a  small 
epicycle  of  one-third  this  eccentricity ;  and,  by  supposing  the 
planet  to  make  two  revolutions  in  this  epicycle  for  every 
revolution  around  the  sun,  he  represented  both  irregulari- 
ties.f 


*  I  have  deduced  these  numbers  from  the  tables  given  in  Book  V.  of  "De 
Revohitionibus  Orbium  CcElestium."  They  are  probably  the  most  accurate  that 
Copernicus  was  able  to  obtain. 

t  The  mathematical  form  of  this  theory  of  Copernicus  is  as  follows :  Putting 


OBLIQUITY  OF  THE  ECLIPTIC.  61 

The  work  of  Copernicus  was  the  greatest  step  ever  taken  in 
astronomy.  But  he  still  took  little  more  than  the  single  step 
of  showing  what  apparent  motions  in  the  heavens  were  real, 
and  what  were  due  to  the  motion  of  the  observer.  Not  only 
was  his  work  in  other  respects  founded  on  that  of  Ptolemy, 
but  he  had  many  of  the  notions  of  the  ancient  philosophy  re- 
specting the  fitness  of  things.  Like  Ptolemy,  he  thought  the 
heavens  as  well  as  the  earth  to  be  spherical,  and  all  the  celes- 
tial motions  to  be  circular,  or  composed  of  circles.  lie  argues 
against  Ptolemy's  objections  to  the  theory  of  the  earth's  mo- 
tion, that  that  philosopher  treats  of  it  as  if  it  were  an  enforced 
or  violent  motion,  entirely  forgetting  that  if  it  exists  it  must 
be  a  natural  motion,  the  laws  of  which  are  altogether  different 
from  those  of  violent  motion.  Tluis,  part  of  his  argument  was 
really  without  scientific  foundation,  though  his  conclusion  was 
correct.  Still,  Copernicus  did  about  all  that  could  have  been 
done  under  the  circumstances.  His  hypothesis  of  a  small  epi- 
cycle one-third  the  eccentricity  represented  the  motions  of  the 
planets  around  the  sun  with  all  the  exactness  that  observation 
then  admitted  of,  while,  in  the  absence  of  any  knowledge  of 
the  laws  of  motion,  it  was  impossible  to  frame  any  dynamical 
basis  for  the  motions  of  the  planets. 

§  2.   Obliquity  of  the  Ecliptic  /  Seasons,  etc.  /  on  the  Coper- 
nican  System. 

"We  have  next  to  explain  the  relations  of  the  ecliptic  and 
equator  on  the  new  system.  Since,  on  this  system,  the  ce- 
lestial sphere  does  not  revolve  at  all,  what  is  the  significance 
of  the  pole  and  axis  around  which  it  seems  to  revolve  ?     The 

e  for  his  eccentricity,  and  g  for  the  mean  anomaly  of  the  planet,  he  represented  its 
rectangular  coordinates  in  the  form 

X—  a  (cos.  g  —  e  -'t^e  cos.  2g\ 

y  =  a  (sin.  ^  +  ^e  sin.  2g) ; 

while  the  approximate  modern  formulae  of  the  elliptic  motion  are — 

X  —  a  (cos.  g  —  %e  +  he  cos.  2g), 

y  —  a  (sin.  g  ■\-  \e  sin.  Ig"), 
wiiich  agree  exactly  when  we  put  e  =  %e. 


C2       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 


Answer  is,  that  the  celestial  poles  are  the  points  among  the  stara 
towards  which  the  axis  of  the  earth  is  directed.  Here  the 
stars  are  supposed  to  be  infinitely  distant,  and  the  axis  of  the 
earth  to  be  continued  in  an  infinite  straight  line  to  meet  them. 
Since  this  point  appears  to  the  unassisted  sight  to  be  the  same 
during  the  entire  year,  it  follows  that  as  the  earth  moves  round 
the  sun,  its  axis  keeps  pointing  in  the  same  absolute  direction, 
as  will  be  shown  in  Fig.  18.  But  in  the  preceding  chapter  we 
showed  that  there  is  a  slow  but  constant  change  in  the  position 
of  the  pole  among  the  stars,  called  precession,  which  the  an- 
cient astronomers  discovered  by  studying  observations  extend- 


Fig.  17.— Relation  of  the  terrestrial  and  celestial  poles  and  equators. 


ing  through  several  centuries,  and  this  shows  that  on  the  Co- 
pernican  system  the  direction  of  the  earth's  axis  is  slowly 
changing. 

To  conceive  of  the  celestial  equator  on  the  Copernican  sys- 
tem, we  must  imagine  the  globular  earth  to  be  divided  into 
two  hemispheres  by  a  plane  intersecting  the  earth  around  its 
equator,  and  continued  out  on  all  sides  till  it  reaches  the  ce- 
lestial sphere.  This  may,  perhaps,  be  better  understood  by 
referring  to  Fig.  17,  representing  the  earth  in  the  centre  of  the 


OBLIQUITY  OF  THE  ECLIPTIC.  63 

imaginary  celestial  sphere.  The  clotted  lines  passing  from  the 
poles  of  the  earth  to  the  points  P  and  S  mark  the  poles  of  that 
sphere.  It  is  evident  that  as  the  earth  turns  on  this  axis,  the 
celestial  sphere,  no  matter  how  great  it  may  seem  to  be,  will 
appear  to  turn  on  the  same  axis  in  the  opposite  direction. 
Again,  ej)  being  the  earth's  equator,  dividing  it  into  two  equal 
parts,  we  have  only  to  imagine  it  to  be  extended  to  E  and  Q^ 
all  round  the  celestial  sphere,  to  cut  the  latter  into  two  equal 
parts. 

Let  us  next  examine  more  closely  the  relation  of  the  earth 
to  the  sun.  We  have  already  shown  that  as  the  earth  moves 
around  the  sun,  the  latter  seems  to  move  around  the  celestial 
sphere,  and  the  circle  in  which  he  seems  to  move  is  called  the 
ecliptic.  But  the  ecliptic  and  the  celestial  equator  are  in- 
clined to  each  other  by  an  angle  of  about  23^°.  This  shows 
that  the  axis  of  the  earth  is  not  perpendicular  to  its  orbit,  but 


^  D 

Fig.  18.— Causes  of  changes  of  seasous  ou  the  Copernican  system. 

is  inclined  231*^  to  that  p>erpendicular,  as  shown  in  Fig.  18, 
which  represents  the  annual  course  of  the  earth  round  the 
sun.  It  is  of  necessity  drawn  on  a  very  incongruous  scale, 
because  the  distance  of  the  sun  fi-om  the  earth  being  near- 
ly 12,000  diameters  of  the  latter  and  110  that  of  the  sun,  both 
bodies  would  be  almost  invisible  if  they  were  not  greatly  mag- 
nified in  the  figure.  A  difiiculty  which  may  suggest  itself  is, 
that  the  present  figure  represents  the  earth  as  moving  away 

6 


6-i       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

from  its  position  in  the  centre  of  tlie  sphere.  There  are  two 
ways  of  avoiding  this  difficulty.  One  is  to  suppose  that  the 
observer  carries  the  imaginary  celestial  sphere  with  him  as  he 
is  carried  around  the  sun;  the  other  is  to  consider  the  sphere 
as  nearly  infinite  in  diameter.  The  latter  is  probably  the 
easiest  mode  of  conception  for  the  general  reader.  He  must, 
therefore,  in  the  last  figure  suppose  the  sphere  to  extend  out 
to  the  fixed  stars,  which  are  so  distant  that  the  whole  orbit  of 
the  earth  is  but  a  point  in  comparison ;  and  the  different  points 
of  the  sphere  towards  which  the  poles  and  the  equator  of  the 
earth  point,  as  the  latter  moves  round  the  sun,  are  so  far  as  to 
appear  always  the  same.  It  now  requires  but  an  elementary 
idea  of  the  geometry  of  the  sphere  to  see  that  these  two  great 
circles  of  tlie  celestial  sphere — the  ecliptic,  around  which  the 
sun  seems  to  move,  and  the  equator,  which  is  everywhere 
equally  distant  from  the  points  in  which  the  earth's  axis  in- 
tersects the  sphere — will  appear  inclined  to  each  other  by  the 
same  angle  by  which  the  earth's  axis  deviates  from  the  per-* 
pendicular  to  the  ecliptic. 

Kext,  we  have  to  see  how  the  changes  of  the  seasons,  the 
equinoxes,  etc.,  are  explained  on  the  Coperuican  theory.  In 
the  last  figure  the  earth  is  represented  in  four  different  posi- 
tions of  its  annual  orbit  around  the  sun.  In  the  position  A^ 
the  south  pole  is  inclined  23i°  towards  the  sun,  while  the 
north  pole,  and  the  whole  region  within  the  arctic  circle,  is 
enveloped  in  darkness.  Hence,  in  this  position,  the  sun  nei- 
ther rises  to  the  inhabitants  of  the  arctic  zone,  nor  sets  to 
those  of  the  antarctic  zone.  Outside  of  these  zones,  he  rises 
and  sets,  and  the  relative  lengths  of  day  and  night  at  any 
place  can  be  estimated  by  studying  the  circles  around  which 
that  place  is  carried  by  the  diurnal  turning  of  the  earth  on  its 
axis.  To  facilitate  this,  we  present  on  the  following  page  a 
magnified  picture  of  the  earth  at  A,  showing  more  fully  the 
hemisphere  in  which  it  is  day  and  that  in  which  it  is  night. 
The  seven  nearly  horizontal  lines  on  the  globe  are  examples 
of  the  circles  in  question.  "We  see  that  a  point  on  the  arctic 
circle  just  grazes  the  dividing-line  between  light  and  darkness 


THE  SEASONS. 


65 


once  in  its  revolution,  or  once  a  day ;  that  is,  the  sun  just 
shows  himself  in  the  horizon  once  a  day.  Of  the  next  circle? 
towards  the  south  about  two- 
thirds  is  in  the  dark,  and  one- 
third  in  the  light  hemisphere. 
This  sliows  that  the  niglits  are 
about  twice  as  long  as  the 
days.  This  circle  is  near  that 
around  which  London  is  carried 
by  the  diurnal  revolution  of  the 
earth  on  its  axis.  As  wc  go 
south,  we  see  that  the  propor- 
tion of  light  on  the  diurnal  cir- 
cles constantly  increases,  while  Fig.IO.- Enlarged  view  of  the  earth  in 
"  ,      ■     •   1  ^^®  positioa  A  of  the  piecediug  figme, 

that  of  darkness  diminishes,  Un-        showing  winter  in  the  northern  hemi- 

til  we  reach  the  equator,  where  '^^'"''  ''^'"^  ''^™'""  ^"  '^^  '°"'^"'°' 
they  are  equal.  When  we  pass  into  the  southern  hemisphere, 
we  see  the  light  covering  more  than  half  of  each  circle,  the 
proportion  of  light  to  darkness  constantly  increasing,  at  the 
same  rate  that  the  opposite  pi'oportion  would  increase  in  going 
to  the  north.  When  we  reach  the  antarctic  circle,  the  whole 
circle  is  in  the  light  hemisphere,  the  observer  just  grazing  the 
dividing-line  at  midnight.  Inside  of  that  circle  the  observer 
Is  in  sunlight  all  the  time,  so  that  the  sun  does  not  set  at  all. 
We  see,  then,  that  at  the  equator  the  days  and  nights  are  al- 
ways of  the  same  length,  and  that  the  inequality  increases  as 
we  approach  either  pole. 

We  now  go  on  three  months  to  the  position  £,  whicli  the 
earth  occupies  in  March.  Here  the  plane  of  the  terrestrial 
equator  being  continued,  passes  directly  through  the  sun  ;  the 
latter,  therefore,  seems  to  be  in  the  celestial  equator.  All  the 
diurnal  circles  are  here  one-half  in  the  illuminated,  and  one- 
half  in  the  unilluminated  hemisphere,  the  latter  being  invisi- 
ble in  the  figure,  through  its  being  behind  the  earth.  The 
days  and  nights  are,  therefore,  of  equal  length  all  over  the 
globe,  if  we  call  it  night  whenever  the  sun  is  geometrically 
below  the  horizon.     In  the  position  O,  which  the  earth  takes 


66       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

in  June,  everything  is  the  same  as  in  position  A^  except  that 
effects  are  reversed  in  the  two  hemispheres.  The  northern 
liemisphere  now  has  the  longest  days,  and  the  southern  one 
the  longest  nights.  At  D,  which  the  earth  reaches  in  Sep- 
tember, the  days  and  nights  are  equal  once  more,  for  the  same 
reason  as  in  £.  Thus,  all  the  seemingly  complicated  phenom- 
ena which  we  have  described  in  the  preceding  chapter  are 
completely  explained  in  the  simplest  way  on  the  new  system. 
We  have  next  to  see  how  the  details  of  the  system  were  filled 
in  by  the  immediate  successors  of  Copernicus. 

§  3.  Tycho  Brake. 

"We  have  said  that  no  great  advance  could  be  made  upon 
the  Copernican  system,  without  either  a  better  knowledge  of 
the  laws  of  motion  or  more  exact  observations  of  the  positions 
of  the  heavenly  bodies.  It  was  in  the  latter  direction  that 
the  advance  was  first  made.  The  leader  was  Tycho  Brahe, 
who  was  born  in  1546,  three  year's  after  the  death  of  Coperni- 
cus. His  attention  was  iii-st  directed  to  the  study  of  astron- 
omy by  an  eclipse  of  the  sun  on  August  21st,  1560,  which  was 
total  in  some  pai-ts  of  Europe.  Astonished  that  such  a  phe- 
nomenon could  be  predicted,  he  devoted  himself  to  a  study  of 
the  methods  of  observation  and  calculation  by  which  the  pre- 
diction was  made.  In  1576  the  King  of  Denmark  founded 
the  celebrated  Observatory  of  Uraniberg,  at  which  Tycho 
spent  twenty  years,  assiduously  engaged  in  observations  of  the 
positions  of  the  heavenly  bodies  with  the  best  instruments  that 
could  then  be  made.  This  was  just  before  the  invention  of 
the  telescope,  so  that  the  astronomer  could  not  avail  himself 
of  that  powerful  instrument.  Consequently,  his  observations 
were  supei*seded  by  the  improved  ones  of  the  centuries  fol- 
lowing, and  their  celebrity  and  importance  are  principally  due 
to  their  having  afforded  Kepler  the  means  of  discovering  his 
celebrated  laws  of  planetary  motion. 

As  a  theoretical  astronomei*,  Tycho  was  unfortunate.  He 
rejected  the  Copernican  system,  for  a  reason  which,  in  his  day, 
had  some  force,  namely,  the  incredible  distance  at  which  it 


TYCHO  BBAHE,  67 

was  necessary  to  suppose  the  fixed  stars  to  be  situated  if  that 
system  were  accepted.  We  have  shown  how,  on  the  Coperni- 
can  system,  the  outer  planets  seem  to  describe  an  annual  revo- 
lution in  an  epicycle,  in  consequence  of  the  annual  revolution 
of  the  earth  around  the  sun.  The  fixed  stars,  which  are  sit- 
uated outside  the  solar  system,  must  appear  to  move  in  the 
sanie  way,  if  the  system  be  correct.  But  no  observations, 
whether  of  Tj^cho  or  his  predecessors,  had  shown  any  such 
motion.  To  this  the  friends  of  Copernicus  could  only  reply 
that  the  distance  of  the  fixed  stars  must  be  so  great  that  the 
motion  could  not  be  seen.  Since  a  vibration  of  three  or  four 
minutes  of  arc  might  have  been  detected  by  Tjxjho,  it  would 
be  necessary  to  suppose  the  stellar  sphere  at  least  a  thousand 
times  the  distance  of  the  sun,  and  a  hundred  times  that  of  Sat- 
urn, then  the  outermost  known  planet.  That  a  space  so  vast 
should  intervene  between  tlie  orbit  of  Saturn  and  the  fixed 
stars  seemed  entirely  incredible:  to  the  philosophers  of  the 
day  it  was  an  axiom  that  nature  would  not  permit  the  waste  of 
space  lieie  implied.  At  the  same  time,  the  proofs  given  by 
Copernicus  that  the  sun  was  the  centre  of  the  planetary  mo- 
tions Mere  too  strong  to  be  overthi-own.  Tycho,  therefore, 
adopted  a  system  which  was  a  compound  of  the  Prulemaic 
and  the  Copernican  ;  he  sn[>posed  the  five  planets  to  move 
around  the  sun  as  the  centre  of  their  motions,  while  the  sun 
was  itself  in  motion,  describing  an  annual  orbit  around  the 
earth,  which  remained  at  rest  in  the  centre  of  the  universe. 

Perhaps  it  is  fortunate  for  the  reception  of  the  Copernican 
system  that  the  astronomical  instruments  of  Tycho  w'ere  not 
equal  to  those  of  the  beginning  of  the  present  century.  Had 
he  found  that  there  was  no  aimual  parallax  among  the  stars 
amounting  to  a  second  of  arc,  and  therefore  that,  if  Coperni- 
cus was  right,  the  stars  must  be  at  least  200,000  times  the  dis- 
tance of  the  sun,  the  astronomical  world  might  have  stood 
aghast  at  the  idea,  and  concluded  that,  after  all,  Ptolemy  must 
be  right,  and  Copernicus  wi-ong. 

Tycho  never  elaborated  his  system,  and  it  is  hard  to  say 
how  he  would  have  answered  the  numerous  objections  to  it. 


6S       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

He  never  had  any  disciples  of  eminence,  except  among  the 
ecclesiastics ;  in  fact,  the  invention  of  the  telescope  did  away 
with  the  last  remaining  doubts  of  the  correctness  of  the  Co- 
pernican  system  before  a  new  one  would  have  had  time  to 
gain  a  foothold. 

§  4.  Kepler. — His  Laws  of  Planeianj  Motion. 

Kepler  was  born  in  1571,  in  Wiirtemberg.  He  was  for  a 
while  the  assistant  of  Tycho  Brahe  in  his  calculations,  but  was 
too  clear-sighted  to  adopt  the  curious  system  of  his  master. 
Seeing  the  truth  of  the  Copernican  system,  he  set  himself  to 
determine  the  true  laws  of  the  motion  of  the  planets  around 
the  sun.  We  have  seen  that  even  Copernicus  had  adopted  the 
ancient  theory,  that  all  the  celestial  motions  are  compounded 
of  uniform  circular  motions,  and  had  thus  been  obliged  to  in- 
troduce a  small  epicycle  to  account  for  the  irregularities  of 
the  motion.  The  observations  of  Tycho  were  so  much  more 
accurate  than  those  of  his  predecessors,  that  they  showed  Kep- 
ler the  insufficienc}'  of  this  theoiy  to  represent  the  true  mo- 
tions of  the  planets  around  the  sun.  The  planet  most  favora- 
ble for  this  investigation  was  Mare,  being  at  the  same  time 
one  of  the  nearest  to  the  earth,  and  one  of  which  the  orbit 
was  most  eccentric.  The  only  way  in  which  Kepler  could 
proceed  in  his  investigation  was  to  make  various  hypotheses 
respecting  the  orbit  in  which  the  planet  moved,  and  its  velocity 
in  various  points  of  its  orbit,  and  from  these  hypotheses  to  cal- 
culate the  positions  and  motions  of  the  planet  as  seen  from 
the  earth,  and  then  compare  with  observations,  to  see  whether 
the  observed  and  calculated  positions  agreed.  As  our  modern 
tables  of  logarithms  b}^  which  such  calculations  are  immensely 
abridged  were  not  then  in  existence,  each  trial  of  an  hypothe- 
sis cost  Kepler  an  immense  amount  of  labor.  Finding  that 
the  form  of  the  orbit  was  certainly  not  circular,  but  elliptical, 
he  was  led  to  try  the  effect  of  placing  the  sun  in  the  focus  of 
the  ellipse.  Then,  the  motion  of  the  planet  would  be  satisfied 
if  its  velocity  were  made  variable,  beinw  m-eater  the  nearer 
it  was  to  the  sun.     Thus  he  was  at  length  led  to  the  first  two 


KEPLER.  69 

of  his  three  celebrated  laws  of  planetary  motion,  which  are  as 
follows : 

1.  The  orbit  of  each  planet  is  an  ellipse ,  having  the  sun  in 
one  focus. 

2.  As  the  planet  moves  round  the  sun,  its  radius-vector  (or 
the  line  joining  it  to  the  sun)  passes  over  equal  areas  in 
equal  times. 

To  explain  these  laws,  let  FA  (Fig.  20)  be  the  ellipse  in 
which  the  planet  moves.    Then  the  sun  will  not  be  in  the  cen- 


Fio.  20.— Illustrating  Kepler's  first  two  laws  of  planetary  motion. 

tre  of  the  ellipse,  bnt  in  one  focus,  say  at  S,  the  other  focus 
beina;  empty.  When  the  planet  is  at  P,  it  is  at  the  point  near- 
est the  sun;  this  point  is  therefore  called  the  perihelion.  As 
it  passes  round  to  the  other  side  of  the  sun,  it  continues  to  re- 
cede from  him  till  it  reaches  the  point  A,  when  it  attains  its 
greatest  distance.  This  point  is  the  aphelion.  Then  it  begins 
to  approach  the  sun  again,  and  continues  to  do  so  till  it  reaches 
P  once  more,  when  it  again  begins  to  repeat  the  same  orbit. 
It  thus  describes  the  same  ellipse  over  and  over. 

Now,  suppose  that,  starting  from  P,  we  mark  the  position 
of  the  planet  in  its  orbit  at  the  end  of  any  equal  intervals  of 
time,  say  30  days,  60  days,  90  days,  120  days,  and  so  on.  Let 
a,  h,  c,  d  be  the  first  four  of  these  positions  between  each  of 
which  the  planet  has  required  30  days  to  move.  Draw  lines 
from  each  of  the  five  positions  of  the  planet,  beginning  at  P^ 


70    SYSTEM  OF  THE   WORLD  HISTOEICALLY  DEVELOPED. 

to  the  sun  at  S.  AVe  shall  thus  have  four  triangular  spaces, 
over  eacli  of  which  the  radius- vector  of  the  planet  lias  swept 
in  30  clays.  The  sectond  law  of  Kepler  means  that  the  areas 
of  all  these  spaces  will  be  equal  to  each  other. 

The  old  theory  that  the  motions  of  the  heavenly  bodies  must 
be  circular  and  uniform,  or,  at  least,  composed  of  circular  and 
uniform  motions,  was  thus  done  away  with  foi'ever.  The  el« 
lipse  took  the  place  of  the  circle,  and  a  variable  motion  the 
place  of  a  uniform  one. 

Another  law  of  planetary  motion,  not  less  important  than 
these  two,  was  afterwards  discovered  by  Kepler.  Coj)erniciis 
knew,  what  had  been  surmised  by  the  ancient  astronomers, 
that  the  more  distant  the  planet,  the  longer  it  took  it  to  per- 
form its  course  around  the  sun,  and  this  not  merely  because  it 
had  farther  to  go,  but  because  its  motion  was  really  slower. 
For  instance,  Saturn  is  about  9^  times  as  far  as  the  earth,  and 
if  it  moved  as  fast  as  the  earth,  it  would  perform  its  revolu- 
tion in  9^  years ;  but  it  actually  requires  between  29  and  30 
yeai-s.  It  does  not,  therefore,  move  one-third  so  fast  as  the 
earth,  although  it  has  nine  times  as  far  to  go.  Copernicus, 
however,  never  detected  any  relation  between  the  distances 
and  the  periods  of  revolution.  Kepler  found  it  to  be  as  fol- 
lows: 

Third  law  of  jilanetary  motion.  The  square  of  the  time 
of  revolution  of  each  planet  in  proportional  to  the  cube  of 
its  mean  distance  from  the  sun. 

This  law  is  shown  in  the  following  table,  which  gives  (1) 
the  mean  distance  of  each  planet  known  to  Kepler,  expressed 
in  astronomical  units,  each  unit  being  the  mean  distance  of 


Planets. 

(1) 
Distance. 

(2) 
Cube  of  Dis- 
tance. 

(3) 
Period 
(Years). 

(4) 

Square  of 

Period. 

Mercury 

Venus 

Earth 

M  a  rs 

0.387 
0.723 
1.000 
1.524 
5.203 
9.539 

0.058 
0.378 
1.000 
3.540 

140.8 

868.0 

0.241 
0.615 
1.000 

1.881 
11.86 
29.46 

0.058 
0.378 
1.001 
3.538 

140.66 

867.9 

Jupiter 

Saturn  

FEOM  KEPLER   TO  NEWTON.  71 

the  earth  from  the  sun ;  (2)  the  cube  of  this  quantity ;  (3)  the 
time  of  revolution  in  years;  and  (4)  the  square  of  this  time. 

The  remarkable  agreement  between  the  second  and  fourth 
columns  will  be  noticed. 

§  5.  From  Kepler  to  Neioton. 

So  far  as  the  determination  of  the  laws  of  planetary  motion 
from  observation  was  concerned,  we  might  almost  say  that 
Kepler  left  nothing  to  be  done.  Given  the  position  and 
magnitude  of  the  elliptic  orbit  in  which  any  planet  moved, 
and  the  point  of  the  orbit  in  which  it  was  found  at  any 
date,  and  it  became  possible  to  calculate  the  position  of  the 
planet  in  all  future  time.  More  than  that  science  could  not 
do.  It  is  true  that  the  places  of  the  planet  thus  predicted 
were  not  found  to  agree  exactly  with  observation ;  and  had 
Kepler  had  at  his  command  observations  as  accurate  as  those 
of  the  present  day,  he  would  have  found  that  his  laws  could 
not  be  made  to  perfectly  represent  the  motion  of  the  planets. 
Not  onl}^  would  the  elliptic  orbit  have  been  found  to  vary  its 
position  from  century  to  century,  but  the  planets  would  have 
been  found  to  deviate  from  it,  first  in  one  direction  and  then 
in  the  other,  wliile  the  areas  described  by  the  radius- vector 
would  have  been  sometimes  larger  and  sometimes  smaller. 
Why  sliould  a  planet  move  in  an  elliptic  orbit  ?  Why  should 
its  radius -vector  describe  areas  proportional  to  tho  time? 
Why  should  there  be  that  exact  relation  between  their  dis- 
tances and  times  of  revolutions?  Until  these  questions  were 
answered,  it  would  have  been  impossible  to  say  why  the  plan- 
ets deviated  from  Kepler's  laws;  and  they  were  questions 
which  it  was  impossible  to  answer  until  the  general  laws  of 
motion,  unknown  in  Kepler's  time,  were  fully  understood. 

The  first  important  step  in  the  discovery  of  these  laws  was 
taken  by  Galileo,  the  great  contemporary  of  Kepler,  one  of 
the  inventors  of  the  telescope,  and  the  first  who  ever  pointed 
that  instrument  at  the  heavens.  From  a  scientific  point  of 
view,  as  inventor  of  the  telescope,  founder  of  the  science  of 
dynamics,  teacher  and  upholder  of  the  Copernican  system,  and 


72       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

sufferer  at  tlie  hands  of  tlie  Inquisition,  for  promulgating  what 
he  knew  to  be  the  truth,  Galileo  is  perhaps  the  most  interest- 
ing character  of  his  time.  If  any  serious  doubt  could  remain 
of  the  correctness  of  the  Copernican  system,  it  was  removed 
by  the  discoveries  made  by  the  telescope.  The  phases  of 
Venus  showed  that  she  was  a  dark  globular  body,  like  the 
earth,  and  that  she  really  revolved  around  the  sun.  In  Jupi- 
ter and  his  satellites,  the  solar  system,  as  described  by  Coperni- 
cus, was  repeated  on  a  small  scale  with  a  fidelity  which  could 
not  fail  to  strike  the  thinking  observer.  There  was  no  longer 
any  opposition  to  the  new  doctrines  from  any  source  entitled 
to  respect.  The  Inquisition  forbade  their  promulgation  as 
absolute  truths,  but  were  perfectly  willing  that  they  should  be 
used  as  ki/j)otheses,  and  rather  encouraged  men  of  science  in 
the  idea  of  investigating  the  interesting  mathematical  prob- 
lems to  which  the  explanation  of  the  celestial  motions  by  the 
Copernican  sj'stem  might  give  rise.  The  only  restriction  was 
that  they  must  stop  short  of  asserting  or  arguing  the  hypothe- 
ses to  be  a  reality.  As  this  assertion  was  implicitly  contained 
in  several  places  in  the  great  work  -of  Copernicus,  they  con- 
demned this  work  in  its  original  form,  and  ordered  its  revi- 
sion.* Probably  the  decree  of  the  Inquisition  was  entirely 
without  effect  in  stopping  the  reception  of  the  Copernican 
system  outside  of  Italy  and  Spain. 

It  will  be  seen,  from  what  has  been  said,  that  the  next  step 
to  be  taken  in  the  direction  of  explaining  the  celestial  motions 
must  be  the  discovery  of  some  general  cause  of  those  motions, 
or,  at  least,  their  reduction  to  some  general  law.  The  first 
attempt  to  do  this  was  made  by  Descartes  in  his  celebrated 
theory  of  vortices,  which  for  some  time  disputed  the  field  with 
Newton's  theory  of  gravitation.  This  philosopher  supposed 
the  sun  to  be  innnersed  in  a  vast  mass  of  fluid,  extending  in- 
definitely in  every  direction.     The  sun,  by  its  rotation,  set  the 

*  The  order  for  this  revision  was  made  at  the  time  of  condemning  Galileo's 
work,  but  I  am  not  aware  that  it  was  ever  executed.  An  edition  of  Copeniicus, 
revised  to  satisfy  the  Inquisition,  would  certainlj'  be  an  interesting  work  to  the 
astronomical  bibliopole  at  the  present  time. 


FROM  KEPLER   TO  NEWTOX.  73 

parts  of  the  fluid  next  to  it  in  rotation ;  these  communicated 
their  motions  to  the  parts  still  farther  out,  and  so  on,  until 
the  whole  mass  was  set  in  rotation  like  a  whii-lpool.  Tlie 
planets  were  carried  around  in  this  ethereal  whirlpool.  The 
more  distant  planets  moved  more  slowly  because  the  ether 
was  less  affected  by  the  rotation  of  the  snn  the  more  distant 
it  was  from  him.  In  the  great  vortex  of  the  solar  system 
were  smaller  ones,  each  planet  being  the  centre  of  one ;  and 
thus  the  satellites,  floating  in  the  ether,  were  carried  round 
their  primaries.  Had  Descartes  been  able  to  show  that  the 
parts  of  his  vortex  must  move  in  ellipses  having  the  sun  in 
one  focus,  that  tliey  must  describe  equal  areas  in  equal  times, 
and  that  the  velocity  must  diminish  as  we  recede  fi-om  the 
sun,  according  to  Kepler's  third  law,  his  theory  would  so  far 
have  been  satisfactory.  Failing  in  this,  it  cannot  be  regarded 
as  an  advance  in  science,  but  rather  as  a  step  backwards.  Yet, 
the  great  eminence  of  tlie  philosopher  and  the  number  of  his 
disciples  secured  a  wide  currency  for  his  theoiy,  and  we  find 
it  supported  by  no  less  an  authority  tlian  John  Bernoulli. 

After  Galileo,  the  man  who,  perhaps,  did  most  to  prepare 
the  way  for  gravitation  was  Iluyghens,  As  a  mathematician, 
a  mechanician,  and  an  observer,  he  stood  in  the  first  rank. 
He  discovered  the  laws  of  centrifugal  force,  and  if  he  had 
simply  applied  these  laws  to  the  solar  system,  he  would  have 
been  led  to  the  result  that  the  planets  are  held  in  their  orbits 
by  a  force  varying  as  the  inverse  square  of  their  distance  from 
the  sun.  Having  found  this,  the  road  to  the  theory  of  gravita- 
tion could  hardly  have  been  missed.  But  the  great  discovery 
seemed  to  require  a  mind  freshly  formed  for  the  occasion. 


74       SYSTEM  OF  THE  WOULD  HISTORICALLY  DEVELOPED, 


CHAPTER  III. 

"CTSTVERSAL    GRAVITATION. 

§  1.  Kewtoru — Discovery  of  Gravitation. 

The  real  significance  of  Xewton's  great  discovery  of  univer- 
sal gravitation  is  fully  appreciated  by  but  few.  Gravitation 
is  ijenerallv  thouo;ht  of  as  a  nivsterious  force,  actinij  onlv  be- 
tween  the  lieavenly  bodies,  and  first  discovei'ed  by  Xewton. 
Had  gravitation  itself  been  discovered  by  Xewton  as  some 
new  principle  to  account  for  the  motions  of  the  planets,  it 
would  not  have  been  so  admirable  a  discovery  as  that  which 
he  actually  made.  Gravitation,  in  a  somewhat  limited  sphere, 
is  known  to  all  men.  It  is  simply  the  force  which  causes 
all  heavy  bodies  to  fall,  or  to  tend  towards  the  centre  of  the 
earth.  Every  one  who  had  ever  seen  a  stone  fall,  or  felt  it  to 
be  heavy,  knew  of  the  existence  of  gravitation.  What  New- 
ton did  was  to  show  that  the  motions  of  the  planets  were 
determined  by  a  univei*sal  force,  of  which  the  force  which 
caused  the  apple  to  fall  was  one  of  the  manifestations,  and 
thus  to  deprive  the  celestial  motions  of  all  tlie  mystery  in 
which  they  had  formerly  been  enshrouded.  To  his  predeces- 
sors, the  continuous  motion  of  the  planets  in  circles  or  ellipses 
was  something  so  completely  unlike  any  motion  seen  on  the 
surface  of  the  earth,  that  they  could  not  imagine  it  to  be  gov- 
erned by  the  same  laws;  and,  knowing  of  no  law  to  limit  the 
planetary  motions,  the  idea  of  the  heavenly  bodies  moving  in 
a  manner  which  set  all  the  laws  of  terrestrial  motion  at  de- 
fiance was  to  them  in  no  way  incredible. 

The  idea  of  a  cosmical  force  emanating  from  the  sun  or  the 
earth,  and  causing  the  celestial  motions,  did  not  originate  with 
K^ewton.  "We  have  seen  that  even  Ptolemy  had  an  idea  of  a 
force  which,  always  directed  towards  the  centre  of  the  earth. 


NEWTON.— DISCOVERY  OF  GRAVITATION.  75 

or,  wliicli  was  to  him  the  same  thing,  towards  the  centre  of 
the  universe,  not  only  caused  licavy  bodies  to  fall,  but  bound 
the  wliole  universe  together.  Kepler  also  maintained  that  the 
force  which  moved  the  planets  resided  in,  and  emanated  from, 
the  sun.  But  neither  Ptolemy  nor  Kepler  could  give  any  ade- 
quate explanation  of  the  force  on  the  basis  of  laws  seen  in  ac- 
tion around  us;  nor  was  it  possible  to  form  any  conception  of  its 
true  nature  without  a  knowledge  of  the  general  laws  of  motion 
and  force,  to  which  neither  of  these  philosopliers  ever  attained. 

The  great  misapprehension  which  possessed  the  minds  of 
nearly  all  mankind  till  the  time  of  Galileo  was,  that  the  con- 
tinuous action  of  some  force  was  necessary  to  keep  a  moving 
body  in  motion.  That  Kepler  himself  was  fully  possessed  of 
this  notion  is  shown  by  the  fact  that  he  conceived  a  force  act- 
ing only  in  the  direction  of  the  sun  to  be  insufficient  for  keep- 
ing up  the  planetary  motions,  and  to  require  to  be  supplement- 
ed by  some  force  which  should  constantly  push  the  planet 
ahead.  The  latter  force,  he  conceived,  might  arise  from  the 
rotation  of  the  sun  on  his  axis.  It  is  hard  to  say  who  was  the 
first  clearly  to  see  and  announce  that  this  notion  was  entirely 
incorrect,  and  that  a  body  once  set  in  motion,  and  acted  on  l)y 
no  force,  would  move  forwards  forever  —  so  gradually  did  tlie 
great  truth  dawn  on  tlie  minds  of  men.  It  must  have  been 
obvious  to  Leonardo  da  Vinci;  it  was  implicitly  contained  in 
Galileo's  law  of  falling  bodies,  and  in  Huyghens's  theory  of 
central  forces;  yet  neither  of  these  philosophers  seems  to  have 
clearly  and  completely  expressed  it.  We  can  hardlj-  be  far 
wrong  in  saying  that  Newton  was  the  first  who  clearly  laid 
down  this  law  in  connect.imi  with  the  correlated  laws  which 
cluster  around  it.  The  basis  of  Newton's  discovery  were  these 
three  laws  of  motion  : 

'  First  law.  A  body  once  set  in  motion  and  acted  on  by  no  force 
will  move  foricards  in  a  straight  line  and  with  a  uniform  velocity 
forever. 

Second  law.  If  a  moving  body  be  acted  on  by  any  force,  its  de- 
viation from  the  motion  defined  in  the  first  law  will  be  in  ih£  direc- 
tion of  the  force,  and  proportional  to  it. 


76        SYSTEM  OF  THE  WOBLD  UISTORICALLY  DEVELOPED. 

Third  law.  Action  and  reaction  are  equal,  and  in  opposite  di- 
rections;  that  is,  U'henever  any  one  hody  exerts  a  force  on  a  second 
one,  the  latter  exerts  a  similar  force  on  the  first,  only  in  the  opposite 
direction. 

The  first  of  these  laws  is  the  fundamental  one.  The  cir- 
cumstance which  impeded  its  disco\ery,  and  set  man  astray 
for  many  centuries,  was  that  there  was  no  body  on  the  earth's 
surface  acted  on  by  no  force,  and  therefore  no  example  of  a 
body  moving  in  a  continuous  straight  line.  Every  body  on 
which  an  experiment  could  be  made  was  at  least  acted  on  by 
the  gravitation  of  the  earth — that  is,  by  its  own  weight — and, 
in  consequence,  soon  fell  to  the  earth.  Other  forces  which  im- 
peded its  motion  were  friction  and  the  resistance  of  the  air. 
It  needed  research  of  a  different  kind  from  what  the  prede- 
cessors of  Galileo  had  given  to  physical  problems  to  show  that, 
but  for  these  forces,  the  body  would  move  in  a  straight  line 
without  hinderance. 

"We  are  now  prepared  to  understand  the  very  straightfor- 
ward and  simple  way  in  which  Xewtou  ascended  from  what 
he  saw  on  the  earth  to  the  great  principle  with  which  his 
name  is  associated.  "We  see  that  there  is  a  force  acting  all 
over  the  earth  by  which  all  bodies  are  drawn  towards  the 
earth's  centre.  This  force  extends  without  sensible  diminu- 
tion, not  only  to  the  tops  of  the  highest  buildings,  but  of  the 
highest  mountains.  How  much  higher  does  it  extend  ?  Why 
should  it  not  extend  to  the  moon  ?  If  it  does,  the  moon  would 
tend  to  drop  to  the  earth,  just  as  a  stone  thrown  from  tlie 
hand  does.  Such  being  the  case,  why  should  not  this  simple 
force  of  gravity  be  the  force  which  keeps  the  moon  in  her 
orbit,  and  prevents  her  from  flying  off  in  a  straight  line  under 
the  first  law  of  motion  ?  To  answer  this  question,  it  was  nec- 
essary to  calculate  what  force  was  requisite  to  retain  the  moon 
in  her  orbit,  and  to  compare  it  with  gravity.  It  was  at  that 
time  well  known  to  astronomers  that  the  distance  of  the  moon 
was  sixty  semidiameters  of  the  earth.  Newton  at  first  sup- 
posed the  earth  to  be  less  than  7000  miles  in  diameter,  and 
consequently  his  calculations  failed  to  lead  him  to  the  right 


NEWTON.— DISCOVERY  OF  GRAVITATION.  77 

result.  This  was  in  1665,  when  he  was  only  twenty  -  three 
years  of  age.  He  laid  aside  his  calculations  for  nearly  twenty 
years,  when,  learning  that  the  measures  of  Picard,  in  France, 
showed  the  earth  to  be  one-sixth  larger  than  he  had  supposed, 
he  agaiu'  took  up  the  subject.  He  now  found  that  the  deflec- 
tion of  the  orbit  of  the  moon  from  a  straight  line  was  such  as 
to  amount  to  a  fall  of  sixteen  feet  in  one  minute,  the  same  dis- 
tance which  a  body  falls  at  the  surface  of  the  earth  in  one 
second.  The  distance  fallen  being  as  the  square  of  the  time, 
it  followed  that  the  force  of  gravity  at  the  surface  of  the  earth 
was  3600  times  as  great  as  the  force  which  held  the  moon  in 
lier  orbit.  This  number  was  the  square  of  60,  which  expresses 
the  number  of  times  the  moon  is  more  distant  than  we  are 
from  the  centre  of  the  earth.  Hence,  the  force  ivliich  holds  the 
moon  in  her  orbit  is  the  same  as  that  ivhich  makes  a  stone  fall^  only 
diminished  in  the  inverse  square  of  the  distance  from  the  centre  of 
the  earth. 

To  the  matliematician  the  passage  from  the  gravitation  of  an 
apple  to  that  of  the  moon  is  quite  simple ;  but  the  non-mathe- 
matical reader  may  not,  at  fii'st  sight,  see  how  the  moon  can  be 
constantly  falling  towards  the  earth  without  ever  becoming  any 
nearer.  The  following  ilhistration  will  make  the  matter  clear : 
any  one  can  understand  the  law  of  falling  bodies,  by  which  a 
body  falls  sixteen  feet  the  first  second,  three  times  that  distance 
the  next,  five  times  the  third,  and  so  on.  If,  in  place  of  falling, 
the  bod}'  bo  projected  horizontally,  like  a  cannon-ball,  for  ex- 
ample, it  will  fall  sixteen  feet  out  of  the  straight  line  in  which 
it  is  projected  during  the  first  second,  three  times  that  distance 
the  next,  and  so  on,  the  same  as  if  dropped  from  a  state  of 
rest.  In  the  annexed  figure,  let  AB  represent  a  portion  of 
the  curved  surface  of  the  earth,  and  AD  a  straight  line  hori- 
zontal at  A,  or  the  line  along  which  an  observer  at  A  Avould 
sight  if  he  set  a  small  telescope  in  a  horizontal  position. 
Then,  owing  to  the  curvature  of  the  earth,  the  surface  will 
fall  aM-ay  from  this  line  of  sight  at  the  rate  of  about  eiglit 
inches  in  the  first  mile,  twenty -four  inches  more  in  the  second 
niile,  and  so  on.     In  five  miles  the  fall  will  amount  to  sixteen 


78       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

feet.     In  ten  miles,  in  addition  to  this  sixteen  feet,  three  times 
that  amount  "will  be  added,  and  so  on,  the  law  being  the  same 

c 


Fig.  21.— Illustratiug  the  fall  of  the  moon  towards  the  earth. 


with  that  of  a  falling  body.  Now,  let  ^C  be  a  high  steep 
mountain,  from  the  summit  of  which  a  cannon-ball  is  fired  in 
the  horizontal  direction  CE.  Tlie  greater  the  velocity  with 
which  the  shot  is  fired,  the  farther  it  will  go  before  it  reaches 
the  ground.  Suppose,  at  length,  that  we  should  fire  it  witli 
a  velocity  of  five  miles  a  second,  and  that  it  should  meet  witli 
no  resistance  from  the  air.  Suppose  e  to  be  the  point  on  the 
line  five  miles  from  C.  Since  it  would  reach  this  point  in  one 
second,  it  follows,  from  the  law  of  falling  bodies  just  cited, 
that  it  will  have  dropped  sixteen  feet  below  e.  But  we  have 
just  seen  that  the  earth  itself  curves  away  sixteen  feet  at  this 
distance.  Hence,  the  shot  is  no  nearer  the  earth  than  when  it 
was  fired.  During  the  next  second,  while  the  ball  would  go  to 
E,  it  would  fall  forty-eight  feet  more,  or  sixty-four  feet  in  all. 
But  here,  again,  the  earth  has  still  been  rounding  off,  so  the 
distance  DB  is  sixty-four  feet.  Hence,  the  ball  is  still  no  near- 
er the  earth  than  when  it  was  fired,  although  it  has  been  drop- 
ping away  from  the  line  in  which  it  was  fired  exactly  like  a 
falling  body.  Moreover,  meeting  with  no  resistance,  it  is  still 
going  on  with  undiminished  velocity;  and,  just  as  it  has  been 
falling  for  two  seconds  without  getting  any  nearer  the  earth, 
so  it  can  get  no  nearer  in  the  third  second,  nor  in  the  fourth, 
nor  in  any  subsequent  second ;  but  the  earth  will  constantly 
curve  away  as  fast  as  the  ball  can  drop.  Thus  the  latter  will 
pass  clear  round  the  earth,  and  come  back  to  the  first  point  C, 


NEWTON.— DISCOVERY  OF  GRAVITATION.  79 

from  which  it  started,  in  the  direction  of  the  arrow,  without 
any  k>ss  of  velocity.  The  time  of  revohition  will  be  about  an 
hour  and  twenty-four  minutes,  and  the  ball  will  thus  keep  on 
revolving  round  the  earth  in  this  space  of  time.  In  other 
w^ords,  the  ball  will  be  a  satellite  of  the  earth,  just  like  the 
moon,  only  much  nearer,  and  revolving  much  faster. 

Our  next  step  is  to  extend  gravitation  to  other  bodies  than 
the  earth.  The  planets  mo\e  around  the  sun  as  the  moon 
does  around  the  earth,  and  must,  therefoi-e,  be  acted  on  by  a 
force  directed  towards  the  sun.  This  force  can  be  no  other 
than  the  gravitation  of  the  sun  itself.  A  very  simple  calcula- 
tion from  Kepler's  third  law  shows  that  the  force  with  which 
each  planet  thus  gravitates  towards  the  sun  is  inversely  as  the 
square  of  the  mean  distance  of  the  planet. 

Only  one  more  step  is  necessary.  AVhat  sort  of  an  orbit 
will  a  planet  describe  if  acted  on  by  a  force  directed  towards 
the  sun,  and  invereely  as  the  square  of  the  distance  ?  A  very 
simple  demonstration  will  show  that,  no  matter  what  the  law 
of  force,  if  it  be  constantly  directed  towards  the  sun,  the  i-adi- 
us- vector  of  the  planet  will  sweep  over  equal  areas  in  equal 
times.  And,  conversely,  it  cannot  sweep  over  equal  areas  in 
equal  times  if  the  force  acts  in  any  other  direction  than  that 
of  the  sun.  Hence  it  follows,  from  Kepler's  second  law,  that 
the  force  is  directed  towards  the  sun  itself. 

The  problem  of  determining  what  form  of  orbit  would  be 
described  was  one  with  which  very  few  mathematicians  of 
that  day  were  able  to  grapple.  Newton  succeeded  in  proving, 
by  a  rigorous  demonstration,  that  the  orbit  would  be  an  el- 
lipse, a  parabola,  or  a  hyperbola,  according  to  circumstances, 
having  the  sun  in  one  of  its  foci,  which,  in  the  case  of  the 
ellipse,  was  Kepler's  first  law.  Thus,  all  mystery  disappeared 
from  the  celestial  motions,  and  the  planets  were  shown  to  be 
simply  heavy  bodies  moving  according  to  the  same  laws  we 
see  acting  all  around  us,  only  under  entirely  different  circum- 
stances. All  three  of  Kepler's  laws  were  expressed  in  the  sin- 
gle law  of  gravitation  towards  the  sun,  with  a  force  acting  in- 
versely as  the  square  of  the  distance. 
E  7 


80       SYSTEM  OF  THE  WORLD  HISTORICALLT  DEVELOPED. 

Very  beautiful  is  the  explanation  -whieli  gravity  gives  of 
Kepler's  third  law.  "We  have  seen  that  if  we  take  the  cubes 
of  the  mean  distances  of  the  several  planets,  and  divide  them 
by  the  square  of  tlie  times  of  revolution,  the  quotient  will  be 
the  same  for  each  planet  of  the  system.  If  we  proceed  in  the 
sam3  way  with  the  satellites  of  Jupiter,  cubing  the  distance 
of  each  satellite  from  Jupiter,  and  dividing  the  cube  by  the 
square  of  the  time  of  revolution,  the  quotient  will  be  the  same 
for  each  satellite,  but  will  not  be  the  same  as  for  the  planets. 
This  quotient,  in  fact,  is  proportional  to  the  mass  or  weiglit  of 
the  central  body.  In  the  case  of  the  planets  it  is  1050  times 
as  great  as  in  the  case  of  the  satellites  of  Jupiter.  This  shows 
that  the  sun  is  1050  times  as  heavy  as  Jupiter.  We  thus  have 
a  very  convenient  way  of  "weighing"  such  of  the  planets  as 
have  satellites,  by  measuring  the  orbits  of  the  satellites,  and 
determining  the  times  of  their  revolution.  But  the  weiorht  is 
not  thus  expressed  in  tons,  but  only  in  fractious  of  the  mass 
of  the  sun. 

The  law,  however,  is  not  yet  complete.  Tlie  attraction  be- 
tween the  sun  and  planets  must,  by  the  third  law  of  motion, 
be  mutual.  If  the  earth  attracts  the  moon,  she  must,  if  the 
law  be  a  general  one,  attract  the  planets  also,  and  the  planets 
must  attract  each  other,  and  thus  alter  their  motions  around 
the  sun.  Xow,  it  is  known  from  observation  that  the  planets 
do  not  move  in  exact  accordance  with  Kepler's  laws.  The 
final  question,  then,  arises  whether  tlie  attraction  of  the  plan- 
ets on  each  other  fully  and  exactly  accounts  for  the  deviations. 
This  question  Newton  could  answer  only  in  an  imperfect  way, 
the  problem  being  too  intricate  for  his  mathematics.  He  was 
able  to  sliow  that  the  attraction  of  the  sun  would  cause  ine- 
qualities in  the  motion  of  the  moon  of  the  same  nature  as 
those  observed,  but  he  could  not  calculate  their  exact  amount. 
Still,  the  general  correspondence  of  his  theory  with  the  mo- 
tions of  the  heavens  was  so  striking  that  there  ought  not  to 
be  any  doubt  of  its  truth.  Very  remarkable,  therefore,  is  it 
to  see  the  French  Academy  of  Sciences,  as  late  as  1732 — more 
than  forty  years  later — awarding  a  prize  to  John  Bernoulli,  the 


GRAVITATION  OF  SMALL  MASSES.  81 

celebrated  mathematician,  for  a  paper  in  which  the  motions 
of  the  planets  were  explained  on  the  theory  of  vortices.  It 
should  not  be  inferred  from  this  that  that  justly  celebrated 
body  still  considered  that  theory  to  be  correct ;  but  we  may 
infer  that  they  still  considered  it  an  open  question  whether 
the  theory  of  gravitation  was  correct. 

To  express  Newton's  theory  with  completeness,  it  is  not  suf- 
ficient to  say  simply  that  the  sun,  earth,  and  planets  attract 
each  other.  Divide  matter  as  finely  as  we  may,  we  find  it 
still  possessing  the  power  of  attraction,  because  it  has  weight. 
Since  the  earth  attracts  the  smallest  particles,  they  must,  by 
the  third  law  of  motion,  attract  the  earth  with  equal  force. 
Hence  we  conclude  that  the  power  of  attraction  resides,  not 
in  the  earth  as  a  whole,  but  in  each  individual  particle  of  the 
matter  composing  it ;  that  is,  the  attraction  of  the  earth  upon 
a  stone  is  simply  the  sum  total  of  the  attractions  between  the 
stone  and  all  the  particles  composing  the  earth. 

There  is  no  known  limit  to  the  distance  to  which  the  at- 
traction of  gravitation  extends.  The  attraction  of  the  sun 
upon  the  most  distant  known  planets,  Uranus  and  Neptune, 
shows  not  the  slightest  variation  from  the  law  of  Newton. 
But,  owing  to  the  rapid  diminution  with  the  distance  to  which 
the  law  of  the  inverse  square  gives  rise  when  we  take  distances 
so  immense  as  those  which  separate  us  from  the  fixed  stars, 
the  gravitation  even  of  the  sun  is  so  small  that  a  million 
years  would  be  required  for  it  to  produce  any  important  ef- 
fect. We  are  thus  led  to  the  law  of  universal  gravitation,  ex- 
pressed as  follows : 

Every  particle  of  matter  in  the  universe  attracts  every  other  par- 
ticle with  a  force  directly  as  their  masses^  and  inversely  as  the 
square  of  the  distance  which  separates  them. 

§  2.  Gravitation  of  Small  Masses. — Density  of  the  Earth. 

To  make  perfect  the  proof  that  gravity  does  really  reside 
in  each  particle  of  matter,  it  was  desirable  to  show,  by  actual 
experiment,  that  isolated  masses  did  really  attract  each  other, 
as  required  by  Newton's   law.     This   experiment  has   been 


82        SYSTEM  OF  THE   WORLD  HISTORICALLY  DEVELOPED. 

made  in  various  ways  with  entire  success,  the  object,  liowev- 
er,  being  not  to  prove  the  existence  of  the  attraction,  but  to 
measure  the  mean  density  of  the  earth,  which  admits  of  be- 
ino-  thus  determined.  The  attraction  of  a  sphere  upon  a  point 
at  its  surface  is  shown,  mathematically,  to  be  the  same  as  if 
the  entire  mass  of  the  sphere  were  concentrated  in  its  centre. 
It  is,  therefore,  directly  as  the  total  amount  of  matter  in  the 
sphere,  that  is,  its  weight,  and  inversely  as  the  square  of  its 
radius.  Let  us,  then,  compare  the  attraction  of  two  spheres  of 
the  same  material,  of  which  the  diameter  of  the  one  is  double 
that  of  the  otlier.  The  larger  will  have  eight  times  the  bulk, 
and  therefore  eight  times  the  mass,  of  tlie  smaller.  But 
against  this  is  the  disadvantage  that  a  particle  on  its  surface 
is  twice  as  far  from  its  centre  as  in  the  case  of  the  smaller 
sphere,  which  causes  a  diminution  of  one -fourth.  Conse- 
quently, it  will  attract  such  a  particle  with  double  the  force 
that  the  smaller  sphere  will ;  that  is,  the  attractions  are  direct- 
ly as  the  diameters  of  the  spheres,  if  the  densities  are  equal. 
If  the  densities  are  not  equal,  the  attraction  is  proportional  to 
the  product  of  the  density  into  the  diameter. 

The  diameter  of  the  earth  is,  in  round  numbers,  forty  millions 
of  feet.  Consequently,  the  attraction  of  a  sphere  of  the  same 
mean  density  as  the  earth,  but  one  foot  in  diameter,  will  be 
40  „io  000  pai't  the  attraction  of  the  earth ;  that  is,  ^^  „i„  ooo 
the  weight  of  the  body  attracted.  Consequently,  if  we  should 
measure  the  attraction  of  such  a  sphere  of  lead,  and  find  that 
it  was  just  4u  ooo  ooo  that  of  the  weight  of  the  body  attracted, 
we  would  conclude  that  the  mean  density  of  the  earth  was 
equal  to  that  of  lead.  But  the  attraction  is  actuall}^  found 
to  be  nearly  twice  as  great  as  this ;  consequently,  a  leaden 
sphere  is  nearly  twice  as  dense  as  the  average  of  the  mat- 
ter composing  the  earth.  Such  a  determination  of  the  density 
of  the  earth  is  known  as  the  Cavendish  experiment,  from  the 
name  of  the  physicist  who  first  executed  it. 

The  method  in  which  a  task  seemingly  so  hopeless  as  meas- 
uring a  minute  force  like  this  is  accomplished  is  shown  in  the 
following  figures.     It  consists  primarily  of  a  torsion  balance ; 


GRAVITATION  OF  SMALL  MASSES. 


83 


that  is,  a  very  light  rod,  e,  with  a  weight  at  each  end,  suspend- 
ed horizontally  by  a  fine  fibre  of  silk.  In  order  to  protect  it 
against  currents  of  air,  it  must  be  completel}'  enclosed  in  a 
case.     In  Fig.  22,  the  balance  eb  is  suspended  from  the  end 


^^  K. 


Fig.  22 Baily's  apparatus  for  determining  the  density  of  the  earth  by  the  Cavendish  ex 

periment.    The  left-hand  ball  b  is  hidden  behind  the  weight  W. 

of  the  arm  KF  by  the  fine  fibi-e  of  silk,  FE.  The  weights  to 
be  attracted  are  at  the  two  ends,  Ih.  When  thus  suspend- 
ed, the  balance  will  swing  round  in  a  horizontal  direction, 
twisting  the  silk  fibre,  by  a  very  small  force.  The  attracting 
masses  consist  of  a  pair  of  leaden  balls,  TFTF,  as  large  as  the 
experimenter  can  procure  and  manage,  which  are  supported 
on  the  turn-table,  T.  In  Fig.  23,  a  view  of  the  apparatus  from 
above  is  given,  showing  the  relative  positions  of  the  leaden 
balls,  and  the  suspended  weights  which  they  are  to  attract. 
It  will  be  seen  that  in  the  position  in  which  the  weights  are 
represented  in  the  figure  their  attraction  tends  to  make  the 
torsion  balance  turn  in  the  direction  opposite  that  of  the  hands 
of  a  watch.  The  effect  of  placing  the  leaden  balls  in  this  posi- 
tion is,  that  the  balance  begins  to  turn  as  described,  and,  being 
carried  by  its  momentum  beyond  the  position  of  equilibrium, 
at  length  comes  to  rest  by  the  twisting  of  the  silk  thread  by 
which  it  is  suspended,  and  then  is  carried  part  of  the  way 


84       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

back  to  its  original  position.  It  makes  several  yibrations, 
each  requiring  some  minutes,  and  at  length  comes  to  rest  in  a 
position  different  from  its  original  one.  The  attracting  balls 
are  then  placed  in  the  reverse  position,  corresponding  to  the 


^Ur- 


v-.-j.,.,-''' 

Fig.  23. — View  of  Bail y's  apparatus  from  above. 

dotted  lines,  so  that  they  tend  to  make  the  balance  swing  in 
the  opposite  direction,  and  the  motions  of  the  balance  are 
again  determined.  These  motions  ai"e  noted  by  a  small  mi- 
croscope, viewed  through  the  enclosure  in  which  the  whole- 
apparatus  is  placed,  and  from  these  motions  the  attractions  oi 
the  balls  can  be  computed. 

Since  this  experiment  was  first  made  by  Cavendish,  it  has 
been  repeated  by  several  otlier  physicists ;  first  by  Professor 
Reich,  of  Freiberg,  in  1S3S,  and  again  by  Francis  Baily,  Esq., 
of  London.  The  latter  repetition  forms  one  of  the  most  elab- 
orate and  exhaustive  series  of  experiments  ever  made;  we 
liave  therefore  chosen  Baily's  apparatus  for  the  purpose  of 
illustration.  The  results  for  the  mean  density  of  the  earth 
obtained  by  these  several  experiments  are: 

Cavendish  (his  own  result) 5.48 

"         (Hutton's  revision) 5.32 

Reich 5.44 

Baily 5.66* 

*  Memoirs  of  the  Royal  Astronomical  Society,  vol.  xix. 


DENSITY  OF  THE  EARTH. 


85 


Fio.  24. 


The  same  problem  has  been  attacked  by  attempting  to  de- 
ternune  the  attraction  of  mountains,  or  portions  of  the  crnst 
of  the  earth.  In  fact,  the  first  attempt 
of  the  sort  ever  made  was  by  Maske- 
lyne,  Astronomer  Koyal  of  Enghvnd 
from  17(56  to  1811,  who  determined 
the  attraction  of  the  mountain  Sche- 
hallien,  in  Scotland,  by  observing  its 
effect  on  the  plumb-line.  The  princi- 
ple of  this  is  very  clear :  on  whichever 
side  of  a  steep  isolated  mountain  we 
hang  a  plumb-line,  the  attraction  of 
the  mountain  will  cause  it  to  incline  towards  it,  the  direction 
of  gravity,  or  the  apparent  vertical,  being  changed  from  AB 
(Fig.  24)^0  AE,  and  from  CD  to  CG.  The  density  of  the 
earth  thus  obtained  was  4.71,  a  quantity  much  smaller  than 
that  afterwards  given  by  the  leaden  balls.  But  this  method 
is  necessarily  extremely  uncertain,  owing  to  the  fact  that  the 
earth  immediately  beneath  the  mountain  will  probably  not  be 
of  the  same  density  as  at  a  distance  from  it,  and  it  is  impos- 
sible to  determine  and  allow  for  this  difference. 

A  third  method  is  to  find  the  change  in  the  force  of  gravity 
as  we  descend  into  the  earth.  We  have  said  that  the  attrac- 
tion of  the  earth  upon  a  point  outside  of  it  is  the  same  as  if 
the  whole  mass  of  the  earth  were  concentrated  in  its  centre. 
Hence,  as  we  rise  above  the  surface  of  the  earth,  thus  reced- 
ing from  the  centre,  the  force  of  gravity  diminishes.  If  this 
force  all  resided  in  the  centre  of  the  earth,  it  would  continue 
to  increase  as  we  went  below  the  surface,  varying  as  the  in- 
verse square  of  our  distance  from  the  centre.  But  such  is  not 
the  case;  because,  once  inside  the  earth, M'e  have  matter  around 
and  above  us,  the  attraction  of  which  lessens  the  gravity  to- 
wards the  centre.  At  the  centre  the  attraction  is  nothing,  be- 
cause a  point  is  there  equally  attracted  in  every  direction.  If 
the  density  of  the  earth  were  uniform,  gravity  would  diminish 
with  perfect  uniformity  from  the  surface  to  the  centre.  But 
in  fact  the  density  of  the  interior  is  so  much  greater  than  that 


86     SYSTEM  OF  THE  WOBLD  HISTORICALLY  DEVELOPED. 

of  the  surface,  tliat  the  force  is  found  to  increase  as  we  go  be- 
low, instead  of  diminisliing.  Professor  Airy,  in  1855,  made 
an  elaborate  series  of  experiments  at  the  Harton  ColHery,  in 
Wales,  in  order  to  obser\e  the  rate  of  increase.  He  found 
that  a  pendulum  at  the  bottom  of  the  mine  went  faster  than 
at  the  top  by  about  2.3  seconds  per  day.  From  this  he  con- 
cluded that  the  mean  density  of  the  earth  was  6.56. 

§  3.  Figure  of  the  Earth. 

If  the  earth  did  not  revolve,  the  mutual  attraction  of  all  its 
parts  would  tend  to  nmke  it  assume  a  spherical  form.  If  the 
cohesion  of  the  solid  parts  prevented  the  spherical  form  from 
being  accurately  assumed,  nevertheless  the  surface  of  the 
ocean,  or  of  any  fluid  covering  the  earth,  would  assume  that 
form.  If,  now,  we  set  such  a  spherical  earth  in  rotation 
around  an  axis,  a  centrifugal  force  will  be  generated  towards 
the  equatorial  regions,  which  will  cause  the  ocean  to  move 
from  the  poles  towards  the  equator,  so  that  the  surface  will 
tend  to  assume  the  form  of  an  oblate  spheroid,  the  longest  di- 
ameter passing  through  the  equator,  and  the  shortest  through 
the  poles.  A  computation  of  the  centrifugal  force  at  the 
equator  shows  it  to  be  -^  the  force  of  gravity  itself.  Conse^ 
quently,  the  oblateness  ought  to  be  easily  measurable  in  gee 
detic  operations.  Yet  another  result  M-as  that,  in  consequence 
of  the  centrifugal  force  at  the  equator,  bodies  would  be  light- 
er, and  a  clock  regulated  to  northern  latitudes  would  lose 
time  when  taken  thither. 

This  last  result  accorded  with  the  experience  of  Richer, 
sent  by  the  French  Academy  to  Cayenne,  in  1672,  to  make  ob- 
servations on  Mars.  After  that,  to  deny  the  oblate  figure  of 
the  earth  was  not  so  much  to  deny  Xewton's  theory  of  gravity 

*  The  general  law  which  regulates  the  force  of  gravity  within  the  earth  is  this: 
The  total  attraction  of  the  shell  of  earth,  wliich  is  outside  the  attracted  point  ex- 
tending all  around  the  globe,  is  notliing,  while  the  remainder  of  tlie  globe,  being 
a  sphere  with  the  point  on  its  surfiice,  attracts  as  if  it  were  all  concentrated  at 
the  centre.  But  tliis  presupposes  that  the  whole  earth  is  composed  of  spherical 
layers,  each  of  uniform  density,  whicii  is  not  strictly  the  case. 


FIGURE  OF   THE  EARTH.  8Y 

as  to  deny  that  mechanical  forces  produced  their  natural  effect 
in  changing  the  form  of  the  surface  of  the  ocean.  Neverthe- 
less, the  French  astronomers  long  refused  their  assent,  because 
the  geodetic  operations  they  had  undertaken  in  France  seemed 
to  indicate  that  the  earth  was  elongated  rather  than  flattened 
in  the  direction  of  the  poles.  The  real  cause  of  this  result 
was,  that  the  distance  measured  in  France  was  so  short  that 
the  effect  of  the  earth's  ellipticity  was  entirely  masked  by  the 
unavoidable  errors  of  the  measures,  yet  it  long  delayed  the  en- 
tire acceptance  of  the  Newtonian  theory  by  the  French  astron- 
omers. We  must,  however,  give  the  latter,  or,  speaking  of 
them  indi\  idually,  their  successors  of  the  next  generation,  the 
credit  of  taking  the  most  thorough  measures  to  settle  the  ques- 
tion. Their  government  sent  one  expedition  to  Peru,  to  meas- 
ure the  length  of  a  degree  of  latitude  at  the  equator,  and  an- 
other to  Lapland,  to  measui-e  one  as  near  as  possible  to  the 
pole.  The  result  was  entirely  in  accord  with  tlie  theory  of 
Newton,  and  gave  it  a  confirmation  which  had  in  the  mean 
time  become  entii-ely  unnecessary. 

Newton  Avas  unable  to  determine  the  exact  figure  which  the 
earth  ought  to  assume  under  the  influence  of  its  own  attrac- 
tion and  the  centrifugal  force  of  rotation,  though  he  could  see 
that  its  meridian  lines  would  be  curves  not  very  different  from 
an  ellipse.  The  complication  of  the  problem  arises  from  the 
fact  that,  as  the  earth  changes  its  form  in  consequence  of  the 
rotation,  the  direction  and  force  of  attraction  at  the  various 
points  of  its  surface  change  also;  and  this,  in  its  turn,  leads 
to  a  different  flgure.  It  was  not  until  the  middle  of  the  last 
century  that  the  problem  of  the  form  of  a  rotating  fluid  mass 
was  solved,  and  the  answer  found  to  be  an  ellipsoid. 

The  figure  of  the  earth  is,  however,  not  an  exact  ellipsoid, 
there  being  two  causes  of  deviation.  (Wlien  we  speak  of  the 
figure  or  dimensions  of  the  earth,  we  mean  those  of  the  ocean 
as  they  would  be  if  the  ocean  covered  the  entire  earth.)  One 
cause  of  deviation  is  that  the  density  of  the  earth  increases 
as  we  approach  its  centre.  The  other  cause  is  that  thei-c  are 
great  irregularities  in  the  density  of  its  superficial  portions. 


JSS       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

Ill  consequence  of  this,  the  real  figure  of  the  water-line  is  full 
of  small  deviations,  ■Nvhicli  are  rendered  very  evident  by  the 
relined  determinations  of  modem  times,  and  which  are  very 
troublesome  to  all  who  are  engaged  in  exact  geodetic  opera- 
tions. 

§  4.  Precession  oftJie  Equinoxes. 

Yet  another  mysterious  phenomenon  which  gravity  com- 
pletely explained  was  that  of  the  precession  of  the  equinoxes. 
"NVe  have  already  described  this  as  a  slow  change  in  the  posi- 
tion of  the  pole  of  the  celestial  spliere  among  the  stars,  lead- 
ing to  a  corresponding  change  in  the  position  of  the  celestial 
equator.  But  the  Copernican  theory  shows  the  celestial  pole 
to  be  purely  fictitious,  because  the  lieavens  do  not  revolve  at 
all,  but  the  earth.  The  pole  of  the  celestial  sphere  is  only 
that  ^x)int  of  the  heavens  towards  which  the  axis  of  the  earth 
points.  Hence,  when  we  come  to  the  Coj^ernican  system,  we 
see  that  precession  must  be  in  the  earth,  and  not  in  the  heav- 
ens, and  must  consist  simply  in  a  change  in  the  direction  of 
the  earth's  axis,  in  virtue  of  which  it  describes  a  circle  in  the 
lieavens  in  about  25,800  yeai-s.  This  effect  was  traced  by 
Xewton  to  the  attraction  of  the  sun  and  moon  on  the  protu- 
berance produced,  as  just  described,  by  the  centrifugal  force 
at  the  earth's  equator.  In  the  present  case  the  effect  is  much 
tlie  same  as  if  the  earth,  being  itself  spherical,  were  enveloped 
by  a  huge  ring  extending  round  its  equator.     In  Fig.  25  let 


Fig.  25. 


AB  represent  this  ring  revolving  around  the  sun,  S;  the  cen- 
trifugal force  of  the  earth,  due  to  its  motion  around  the  sun, 
will  then  balance  the  mean  attraction  of  the  sun  upon  it.  But 
the  point  A  being  near  the  sun,  the  attraction  of  the  latter  upon 


PRECESSION  OF  THE  EQUINOXES.  89 

it  will  be  more  powerful  than  upon  C,  and  consequently  great- 
er than  the  centrifugal  force.  So  thei-e  will  be  a  surplus  force 
drawing  A  towards  the  sun.  At  B  the  attractive  force  of  tlie 
sun  is  less  than  the  mean,  so  that  there  is  a  surplus  force  tend- 
ing to  draw  B  from  the  sun.  The  ring  being  oblique  towards 
the  sun,  the  effect  of  these  surplus  forces  would  be  to  make 
the  ring  turn  round  on  c  until  the  line  vl5  pointed  towards  the 
sun.  The  spherical  earth  beiDg  fastened  in  the  ring,  as  just 
supposed,  would  very  slowlj'  be  turned  round  with  the  ring,  so 
that  its  equator  would  be  directed  towards  the  sun.  But  this 
effect  is  prevented  by  the  earth's  rotation  on  its  axis,  which 
makes  it  act  like  a  gyroscope,  or  like  a  spinning-top.  Instead 
of  being  brought  down  towards  the  sun,  a  very  slow  motion,  at 
right  angles  to  tliis  direction,  is  produced,  and  thus  we  have 
the  motion  of  p-.ccession.  The  nature  of  this  motion  may  be 
best  seen  by  Fig.  18,  where  the  north  pole  of  the  earth  is  rep- 
resented as  constantly  inclined  to  the  right  of  the  observer  as 
the  earth  n^oves  i-ound  the  sun,  so  that  the  solstices  are  at  A 
and  C,  a\id  the  equinoxes  at  B  and  D.  The  effect  of  the  at- 
traction of  the  sun  and  moon  on  the  protuberance  at  the 
equator  is,  that  in  6500  years  the  axis  of  the  earth  will  incline 
towards  the  observer  of  the  picture,  with  nearly  the  inclina- 
tion of  23° ;  so  that  the  solstices  will  be  at  B  and  D,  and  the 
equinoxes  at  A  and  C.  In  6500  years  more  the  north  pole 
will  be  pointed  towards  the  left  instead  of  the  right,  as  in  the 
figure;  in  6500  more  it  will  be  directed  from  the  observer; 
and,  finally,  at  the  end  of  a  fourth  period  it  will  be  once  more 
near  its  present  position. 

The  effects  we  have  described  ^vould  not  occur  if  the  plane 
of  the  ring,  AB,  passed  through  the  sun,  because  then  the 
forces  which  draw  A  towards  the  sun  and  B  from  it,  would  act 
directly  against  each  other,  and  so  destroy  each  other's  effect. 
Now,  this  is  the  case  twice  a  year,  namely,  when  the  sun  is  on 
the  equator.  Therefore,  the  motion  of  precession  is  not  uni- 
form, but  is  much  greater  than  the  average  in  June  and  De- 
cember, when  the  sun's  declination  is  greatest ;  and  is  less  in 
March  and  September,  when  the  sun  is  on  the  plane  of  the 


90       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

equator.  Moreover,  in  December  the  earth  is  nearer  the  sun 
than  in  June,  and  the  force  greater,  so  that  we  have  still  an- 
otlier  inequality  from  this  cause. 

Precessiun  is  not  produced  by  the  sun  alone.  The  moon  is 
a  yet  more  powerful  agent  in  producing  it,  its  smaller  mass 
being  more  than  compensated  by  its  greater  pro.ximity  to  us.* 
The  same  causes  which  make  the  action  of  the  sun  variable 
make  that  of  the  moon  variable  also,  and  we  have  the  addi- 
tional cause  that,  owing  to  the  revolution  of  the  moon's  node, 
the  inclination  of  the  moon's  orbit  to  the  plane  of  the  earth's 
equator  is  subject  to  an  oscillation  having  a  period  of  18.6 
years,  producing  an  inequality  of  this  same  period  in  the  pre- 
cession. The  several  inequalities  in  the  precession  which  we 
have  described  are  known  as  mdation  of  the  earth's  axis,  and 
are  all  accurately  computed  and  laid  down  in  astronomical 
tables. 

§  5.  The  Tides. 

It  has  been  known  to  seafaring  nations  from  a  remote  an- 
tiquity that  there  was  a  singular  connection  between  tiie  ebb 
and  flow  of  the  tides,  and  the  diurnal  motion  of  the  moon. 
Caesar's  description  of  his  passages  across  the  English  Channel 
shows  that  he  was  acquainted  with  the  law.  In  describing 
the  motion  of  the  moon,  it  was  shown  that,  owing  to  her  revo- 
lution in  a  monthly  orbit,  she  rises,  passes  the  meridian,  and 
sets  abor.t  fifty  minutes  later  every  day.  The  tides  ebb  and 
flow  twice  a  day,  but  the  corresponding  tide  is  always  later 
than  the  day  before,  by  the  same  amount,  on  the  avei-age.  that 
the  moon  is  later.  Hence,  at  any  one  place,  the  tides  always 
occur  when  the  moon  is  near  the  same  point  of  her  appaient 
dimnal  course. 


*  This  may  need  some  explanation,  as  tlie  attractive  force  of  tlie  sun  upon  the 
earth  is  more  than  a  hundred  times  that  of  tlie  moon.  The  force  which  produces 
precession  is  proportional  to  the  difference  of  the  attractions  on  the  two  sides  of 
the  earth,  or  on  A  and  B  in  Fig.  2"),  and  this  difference  is  greater  in  the  case  of 
the  moon's  attraction.  In  fact,  it  varies  inversely  as  the  cube  of  the  distance  ot 
the  attracting  body. 


THE  TIDES.  91 

Tlie  cause  of  this  ebb  and  flow  of  the  sea,  and  its  relation 
to  tlie  moon,  was  a  mystery  until  gravitation  showed  it  to  be 
due  to  the  attraction  of  the  moon  on  the  waters  of  the  ocean. 
The  reason  why  there  are  two  tides  a  day  will  appear  by 
studying  the  case  of  the  moon's  revolution  around  the  earth. 
Let  M  be  the  moon,  ^  the  earth,  and  EMi\\c.  line  joining  their 
centres.  Now,  strictly  speaking,  the  moon  does  not  revolve 
around  the  earth,  any  more  than  the  earth  around  the  moon ; 
but  by  the  principle  of  action  and  reaction  the  centre  of  each 
body  moves  around  the  common  centre  of  gravity  of  the  two 
bodies.  The  earth  being  eighty  times  as  heavy  as  the  moon, 
this  centre  is  situated  within  the  former,  about  three-quarters 
of  the  way  from  its  centre  to  its  surface,  at  the  point  G  in  the 


A 

Fig.  26. — Attraction  of  the  moou  tending  to  produce  tides. 

figure.  The  body  of  the  earth  itself  being  solid,  every  part  of 
it,  in  consequence  of  the  moon's  attraction,  may  be  considered 
as  describing  a  circle  once  in  a  month,  having  a  radius  equal 
to  EG.  The  centrifugal  force  caused  by  this  rotation  is  just 
balanced  by  the  mean  attraction  of  the  moon  upon  the  earth. 
If  this  attraction  were  the  same  on  every  part  of  the  earth, 
there  would  be  everywhere  an  exact  balance  between  it  and 
the  centrifugal  force.  But  as  we  pass  from  E  to  I)  the  at- 
traction of  the  moon  diminishes,  owing  to  tlie  increased  dis- 
tance. Hence  at  D  the  centrifugal  force  predominates,  and 
the  water  therefore  tends  to  move  away  from  the  centre  E. 
As  we  pass  from  E  towards  C  the  attraction  of  tlie  moon  in- 
creases, and  therefore  exceeds  the  centrifugal  force.  Conse- 
quently, at  C  there  is  a  tendency  to  draw  the  water  towards 
the  moon,  but  still  away  from  the  centre  E.  At  A  and  B  the 
attraction  of  the  moon  increases  the  gravity  of  the  water,  ow- 


92    SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

ing  to  the  convergence  of  the  lines  ^Jf  and  AM,  along  which 
it  acts ;  hence  the  action  of  the  raoon  tends  to  make  the  waters 
rise  at  D  and  C,  and  to  fall  at  A  and  B ;  there  are  therefore 
two  tides  to  each  apparent  diurnal  revolution  of  the  moon. 

If  the  waters  everywhere  yielded  immediately  to  the  at- 
tractive force  of  the  moon,  it  would  always  be  high -water 
when  the  moon  was  on  the  meridian,  low-water  when  she  was 
rising  or  setting,  and  high-water  again  when  she  was  in  the 
middle  of  that  portion  of  her  course  which  is  under  the  hori- 
!?;on.  But,  owing  to  the  inertia  of  the  water,  some  time  is 
necessary  for  so  slight  a  force  to  set  it  in  motion,  and,  once  in 
motion,  it  continues  so  after  the  force  has  ceased,  and  until  it 
has  acted  some  time  in  the  opposite  direction.  Therefore,  if 
the  motion  of  the  water  were  unimpeded,  it  would  not  be 
high-water  until  some  hours  after  the  moon  had  passed  the 
meridian.  Yet  another  circumstance  interferes  with  the  free 
motion  of  the  water  —  namely,  the  islands  and  continents. 
These  deflect  the  tidal  wave  from  its  course  in  such  a  way  that 
it  may,  in  some  cases,  be  many  hours  behind  its  time,  or  even 
a  whole  day.  Sometimes  two  waves  may  meet  each  other, 
and  raise  an  extraordinarily  high  tide.  At  other  times  the 
tides  may  have  to  run  up  a  long  bay,  where  the  motion  of  a 
long  mass  of  water  will  cause  an  enormous  tide  to  be  raised. 
In  the  Bay  of  Fnndy  both  of  these  causes  are  combined.  A 
tidal  wave  coming  up  the  Atlantic  coast  meets  the  ocean 
wave  from  the  east,  and,  entering  the  bay  with  their  com- 
bined force,  the  water  at  the  head  of  it  is  forced  up  to  the 
height  of  sixty  or  seventy  feet,  on  the  principle  seen  in  the 
hydraulic  ram. 

The  sun  produces  a  tide  as  well  as  the  moon,  the  force 
which  it  exerts  on  the  two  sides  of  the  earth  being  the  same, 
which,  acting  on  the  equatorial  protuberance  of  the  earth, 
produces  precession.  The  tide-producing  force  of  the  sun  is 
about  -py  of  that  of  the  moon.  At  new  and  full  moon  the  two 
bodies  unite  their  forces,  and  the  result  is  that  the  ebb  and 
flow  are  greater  than  the  average,  and  we  have  the  "  spring- 
tides."    "When  the  moon  is  in  her  first  or  third  quarter,  the 


INEQUALITIES  IN  THE  MOTIONS  OF  THE  PLANETS.       93 

two  forces  act  against  each  other;  the  tide-producing  force  is 
the  difference  of  the  two,  the  ebb  and  flow  are  less  than  the 
average,  and  we  have  the  "  neap-tides." 

§  6.  Inequalities  in  the  Motions  of  the  Planets  produced  hy  their 
Mutual  Attraction. 

The  profoundest  question  growing  out  of  the  theory  of 
gravitation  is  whether  all  the  inequalities  in  the  motion  of  the 
moon  and  planets  admit  of  being  calculated  from  their  mut- 
ual attraction.  This  question  can  be  completely  answered 
only  by  actually  making  the  calculation,  and  seeing  whether 
the  resulting  motion  of  each  planet  agrees  exactly  with  that 
observed.  The  problem  of  computing  the  motion  of  each 
planet  under  the  influence  of  the  attraction  of  all  the  others 
is,  however,  one  of  such  complexity  that  no  complete  and  per- 
fect solution  has  ever  been  found.  Stated  in  its  most  general 
form,  it  is  as  follows :  Any  number  of  planets  of  which  tlie 
masses  are  known  are  projected  into  space,  their  positions,  ve- 
locities, and  directions  of  motion  all  being  given  at  some  one 
moment.  They  are  then  left  to  their  mutual  attractions,  ac- 
cording to  the  law  of  gravitation.  It  is  required  to  find  gen- 
eral algebraic  formulae  by  which  their  position  at  any  time 
whatever  shall  be  determined.  In  this  general  form,  no  ap- 
proximation to  an  entire  solution  has  ever  been  found.  But 
the  orbits  described  by  the  planets  around  the  sun,  and  by  the 
satellites  around  their  primaries,  are  nearl}'  circular ;  and  this 
circumstance  affords  the  means  of  computing  the  theoretical 
place  of  the  planet  as  accurately  as  we  please,  provided  the 
necessary  labor  can  be  bestowed  upon  the  work. 

Wliat  makes  the  problem  so  complex  is  that  the  forces 
Avliich  act  upon  the  planets  are  dependent  on  their  motions, 
and  these  again  are  determined  by  the  forces  which  act  on 
them.  If  tlie  planets  did  not  attract  each  other  at  all,  the 
problem  could  be  perfectly  solved,  because  they  would  then 
all  move  in  ellipses,  in  exact  accordance  with  Kepler's  laws. 
Supposing  them  to  move  in  ellipses,  their  positions  and  dis- 
tances at  any  time  could  be  expressed  in  algebraic  formula3, 


94       SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

and  their  attractions  on  each  other  could  be  expressed  in  the 
same  way.  But,  owing  to  these  very  atti-actions,  they  do  not 
move  in  ellipses,  and  therefore  the  formulse  thus  found  will 
not  be  strictly  correct.  To  put  the  difficulty  iuto  a  nut-shell, 
the  geometer  cannot  strictly  determine  the  motion  of  the  plan- 
et until  he  knows  the  attractions  of  all  the  other  planets  on  it, 
and  he  cannot  determine  these  without  first  knowing  the  posi- 
tion of  the  planet,  that  is,  without  having  solved  his  problem. 

The  question  how  to  surmount  these  difficulties  has,  to  a 
greater  or  less  extent,  occupied  the  attention  of  all  great  math- 
ematicians from  the  time  of  Newton  till  now ;  and  although 
complete  success  has  not  attended  their  efforts,  yet  the  mar- 
vellous accuracy  with  which  sun,  moon,  and  planets  move  in 
their  prescribed  orbits,  and  the  certainty  with  which  the  laws 
of  variation  of  those  orbits  through  countless  ages  past  and  to 
come  have  been  laid  down,  show  that  tlieir  labor  has  not  been 
in  vain.  Xewton  could  attack  the  problem  only  in  a  geomet- 
rical way ;  he  laid  down  diagrams,  and  showed  in  what  way 
the  forces  acted  in  various  parts  of  the  orbits  of  the  two  plan- 
ets, or  in  various  positions  of  the  sun  and  moon.  He  was  thus 
enabled  to  show  how  the  attraction  of  the  sun  upon  the  moon 
changes  the  orbit  of  the  latter  around  the  earth,  and  causes  its 
nodes  to  revolve  from  east  to  west,  as  observations  had  shown 
them  to  do,  and  to  calculate  roughly  one  or  two  of  the  inequal- 
ities in  the  motion  of  the  moon  in  her  orbit. 

When  the  Continental  mathematicians  were  fully  convinced 
of  the  correctness  of  Xewton's  theory,  they  immediately  at- 
tacked the  problem  of  planetary  motion  with  an  energy  and 
talent  which  placed  them  ahead  of  the  rest  of  the  world. 
They  saw  the  entire  insufficiency  of  Xewton's  geometrical 
method,  and  the  necessity  of  having  the  forces  which  moved 
the  planets  expressed  by  the  algebraic  method,  and,  by  adopt- 
xws.  this  svstem,  were  enabled  to  go  far  ahead  both  of  Xew- 
ton  and  his  countrymen.  The  last  half  of  tlie  last  century 
was  the  Golden  Age  of  mathematical  astronomy.  Five  il- 
lustrious names  of  this  period  outshine  all  otliers:  Clairaut, 
D'Alembert,  Euler,  Lagrange,  and  Laplace,  all,  except  Euler, 


INEQUALITIES  IN  THE  MOTIONS   OF  THE  PLANETS.       95 

French  by  birth  or  adoption.  The  great  works  which  closed 
it  were  the  "  Mecanique  Celeste  "  of  Laplace,  and  the  "  Me- 
caniqne  Analytique"  of  Lagi-ange,  which  embody  the  sub- 
stance of  all  that  was  then  known  of  the  subject,  and  form  the 
basis  of  nearly  everything  that  has  since  been  achieved.  We 
shall  briefly  mention  some  of  the  results  of  these  woiks,  and 
those  of  their  successors  which  may  interest  the  non- mathe- 
matical reader. 

Perliaps  the  most  striking  of  these  results  is  that  of  the  sec- 
ular variations  of  the  planetary  orbits.  Copernicus  and  Kep- 
ler had  found,  by  comparing  the  planetary  orbits  as  observed, 
by  themselves  with  those  of  Ptolemy-,  that  the  forms  and  posi- 
tions of  those  orbits  were  subject  to  a  slow  change  from  cen- 
tury to  century.  The  innnediate  successors  of  Newton  were 
able  to  trace  this  change  to  the  mutual  action  of  the  planets, 
and  thus  arose  the  important  question,  Will  it  continue  for- 
ever? For,  should  it  do  so,  it  would  end  in  the  ultimate  sub- 
version of  the  solar  system,  and  the  destruction  of  all  life  on 
our  globe.  The  orbit  of  the  earth,  as  well  as  of  the  other  plan- 
ets, would  become  so  eccenti'ic  that,  approaching  near  tlie  sun  at 
one  time,  and  receding  far  from  it  at  another,  the  vicissitudes 
of  temperature  would  be  insupportable.  Lagrange,  however, 
was  enabled  to  show  by  a  nmtliematical  demonstration  that 
these  changes  were  due  to  a  regular  system  of  oscillations  ex- 
tending throughout  the  whole  planetary  system,  the  periods  of 
which  were  so  immensely  long  that  only  a  progressive  motion 
could  be  perceived  during  all  the  time  that  men  had  observed 
the  planets.  The  number  of  these  combined  oscillations  is 
equal  to  that  of  the  planets,  and  their  periods  range  from 
50,000  years  all  the  way  up  to  2,000,000— "  Great  clocks  of 
eternity,  which  beat  ages  as  ours  beat  seconds."  Iti  conse- 
quence of  these  oscillations,  the  perihelia  of  the  planets  will 
turn  in  every  direction,  and  the  orbits  will  vary  in  eccentricity, 
but  will  never  become  so  eccentric  as  to  disturb  the  regularity 
of  the  system.  About  18,000  years  ago,  the  eccentricity  of  the 
earth's  orbit  was  about  .019 ;  it  has  been  diminishinjr  ever 
since,  and  will  continue  to  diminish  for  25,000  years  to  come, 

8 


96       SYSTEM  OF  TEE  WOULD  HISTOBICALLY  DEVELOPED. 

when  it  will  be  more  nearly  a  circle  than  any  orbit  of  onr  sys- 
tem now  is. 

Some  of  the  questions  growing  out  of  the  moon's  motion 
are  not  completely  settled  yet.  Early  in  the  last  century  it 
was  found  by  Halley,  from  a  comparison  of  ancient  eclipses 
with  modern  observations  of  the  moon,  that  our  satellite  was 
accelerating  her  motion  around  the  earth.  She  was,  in  fact, 
about  a  degree  ahead  of  where  she  ought  to  have  been  had 
her  motion  been  uniform  from  the  time  of  Hipparchus  and 
Ptolemy.  The  existence  of  this  acceleration  was  fulh'  estab- 
lished in  the  time  of  Lagrange  and  Laplace,  and  was  to  them 
a  source  of  great  perplexity,  because  they  had  conceived  them- 
selves to  have  shown  mathematically  that  the  mutual  attmc- 
tions  of  the  planets  or  satellites  could  never  accelerate  or  re- 
tard their  mean  motions  in  their  orbits,  and  thus  the  motion 
of  the  moon  seemed  to  be  affected  by  some  other  force  than 
gravitation.  After  several  vain  attempts  to  account  for  the 
motion,  it  was  found  by  Laplace  that,  in  consequence  of  the 
secular  diminution  of  the  eccentricity  of  the  earth's  orbit,  the 
action  of  the  sun  on  the  moon  was  progressively  changing  in 
such  a  manner  as  to  accelerate  its  motion.  Computing  the 
amount  of  the  acceleration,  he  found  it  to  be  about  10  sec- 
onds in  a  century,  and  its  action  on  the  moon  being  like  that 
of  gravity  on  a  falling  body,  the  total  effect  would  increase  as 
the  square  of  the  time ;  that  is,  while  in  one  century  the  moon 
would  be  10  seconds  ahead,  in  two  centuries  she  would  be  40 
seconds  ahead,  in  three  centuries  90  seconds,  and  so  on. 

This  result  agreed  so  well  M'ith  the  observed  acceleration, 
as  determined  by  a  comparison  of  ancient  eclipses  with  mod- 
ern data,  that  no  one  doubted  its  correctness  till  long  after  the 
time  of  Laplace.  But,  in  1853,  Mr.  J.  C.  Adams,  of  England, 
celebrated  as  one  of  the  two  mathematicians  who  had  calcu- 
lated the  position  of  Xeptune  from  the  motions  of  L^ranus,  un- 
dertook to  recompute  the  effect  of  the  variation  of  the  earth's 
eccentricity  on  the  mean  motion  of  the  moon.  Pie  was  sur- 
prised to  find  that,  carrying  his  process  farther  than  Laplace 
had  done,  the  effect  in  question  was  reduced  from  10  seconds, 


INEQUALITIES  IN  THE  MOTION  OF  THE  MOON.  97 

the  result  of  Laplace,  to  6  seconds.  On  the  other  hand,  the 
further  examination  of  ancient  and  modern  observations 
seemed  to  show  that  the  acceleration  as  given  by  them  wai 
even  greater  than  that  found  by  Laplace,  being  more  nearly 
12  seconds  than  10  seconds ;  that  is,  it  was  twice  as  great  as 
that  computed  by  Mr.  Adams  from  the  theory  of  gravitation. 

The  announcement  of  this  result  by  Mr.  Adams  was  at  fi)'st 
received  with  surprise  and  incredulity,  and  led  to  one  of  the 
most  remarkable  of  scientific  discussions.  Three  of  the  great 
astronomical  mathematicians  of  the  day — Hansen,  Plana,  and 
De  Pontecoulant  —  disputed  the  correctness  of  Mr.  Adams's 
result,  and  maintained  that  that  of  Laplace  was  not  affected 
with  any  such  error  as  Mr.  Adams  had  found.  In  fact,  Hansen, 
by  a  metliod  entirely  different  from  that  of  his  predecessors, 
had  found  a  result  of  12  seconds,  which  was  yet  larger  than 
that  of  Laplace.  On  the  other  hand,  Delaunay,  of  Paris,  by  a 
new  and  ingenious  method  of  his  own,  found  a  result  agreeing 
exactly  with  Mr.  Adams's.  Thus,  the  five  leading  experts  of 
the  day  were  divided  into  two  parties  on  a  purely  mathemat- 
ical question,  and  several  years  were  required  to  settle  the  dis- 
pute. The  majority  had  on  their  side  not  only  the  facts  of 
observation,  so  far  as  they  went,  but  the  authority  of  Laplace; 
and,  if  the  question  could  have  been  settled  either  by  observa- 
tion or  by  authority,  they  must  have  carried  the  day.  But  the 
problem  was  altogether  one  of  pure  mathematics,  depending 
on  the  computation  of  the  effect  M^hich  the  gravitation  of  the 
sun  ought  to  produce  on  the  motion  of  the  moon.  Both  par- 
ties were  agreed  as  to  the  data,  and  but  one  correct  result  was 
possible,  so  that  an  ultimate  decision  could  be  reached  only  by 
calculation. 

The  decision  of  such  a  question  could  not  long  be  delayed. 
There  was  really  no  agreement  among  the  majority  as  to  what 
the  supposed  error  of  Mr.  Adams  consisted  in,  or  what  the  ex- 
act mathematical  expression  for  the  moon's  acceleration  was. 
On  the  other  hand,  Mr.  Adams  showed  conclusively  tliat  the 
methods  of  De  Pontecoulant  and  Plana  were  fallacious;  and  the 
more  profoundly  the  question  was  examined,  the  more  evident 


98     SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

it  became  that  he  was  right.  Mr.  Cayley  made  a  computation 
of  the  result  by  a  new  method,  and  Delaunay  by  yet  another 
.method,  and  both  agreed  with  Mr,  Adams's.  Although  their 
antagonists  never  formally  surrendered,  they  tacitly  abandon- 
ed the  iield,  leaving  Delaunay  and  Adams  in  its  undisturbed 
possession.* 

It  was  thus  conclusively  settled  that  the  true  value  of  the 
acceleration  was  about  6",  the  last  value  found  by  Delaunay 
being  6".18.  This  result  was  only  about  half  of  that  which 
had  been  derived  from  the  observations  of  ancient  eclipses,  so 
that  there  appeared  to  be  a  discrepancy  between  the  observed 
and  the  theoretical  acceleration,  the  cause  of  which  was  to 
be  investigated.  A  possible  cause  happened  to  be  already 
known :  the  friction  of  the  tidal  wave  nmst  constantly  retard 
the  diurnal  motion  of  the  earth  on  its  axis,  though  it  is  impos- 
sible to  say  how  much  this  retardation  may  amount  to.  The 
consequence  would  be  that  the  day  would  gradually,  but  un- 
ceasingly, increase  in  length,  and  our  count  of  time,  depend- 
ing on  the  day,  would  be  always  getting  too  slow.  The  moon 
would,  therefore,  appear  to  be  going  faster,  when  really  it  was 
only  the  earth  which  was  moving  more  slowly.  So  long  as 
theory  had  agreed  with  the  observed  acceleration  of  the  moon, 
there  had  been  no  need  to  invoke  this  cause ;  but,  now  that 
there  was  a  difference,  it  afforded  the  most  plausible  explana- 
tion. 

Thus  the  theory  of  the  subject  is  that  there  is  an  undoubted 
real  acceleration  of  6'M8,  and  an  additional  apparent  accel- 
eration of  a  few  seconds,  due  to  the  tidal  retardation  of  the 
earth's  rotation,  the  amount  of  which  can  be  found  only  by 
comparing  the  motions  of  the  moon  in  different  centuries. 
The  absence  of  precise  observations  in  ancient  times  renders 
this  determination  difficult  and  uncertain.  The  ancient  rec- 
ords which  have  been  most  relied  on  are  the  nai-ratives  of  sup- 

*  The  writer  has  reason  to  believe  it  an  historical  fact  that  Hansen,  on  revising 
his  own  calculations,  and  including  terms  he  at  first  supposed  to  be  insensible, 
found  that  he  would  be  led  substantially  to  the  result  of  Adams,  although  he 
never  made  any  formal  publication  of  this  fact. 


INEQUALITIES  IN  THE  MOTION  OF  THE  MOON.  99 

posed  total  eclipses  of  the  sun,  which  have  been  handed  down 
to  us  by  the  Greek  and  Roman  classical  writers.  The  most 
ancient  and  celebrated  of  these  eclipses  is  associated  with  the 
name  of  Thales,  the  Ionian  philosopher,  our  knowledge  of 
which  is  derived  from  the  following  account  by  Herodotus : 

"  Now  after  this  (for  Alyattes  did  not  by  any  means  sur- 
render the  Scythians  at  the  demand  of  Cyaxares)  there  was 
war  between  the  Lydians  and  the  Medes  for  the  space  of  five 
years,  in  which  [period]  the  Medes  often  conquered  the  Lydi- 
ans, and  the  Lydians,  in  turn,  the  Medes.  And,  in  this  time, 
they  also  had  a  niglit  engagement;  for  as  they  were  protract- 
ing the  war  with  equal  success  on  each  side,  in  a  battle  that 
occurred  in  the  sixth  year,  it  happened,  as  the  armies  en- 
gaged, that  the  day  was  suddenly  turned  into  night.  Now 
this  change  of  the  day  [into  night]  Thales,  the  Milesian,  had 
predicted  to  the  lonians,  placing  as  the  limit  of  the  period 
[within  which  it  would  take  place]  this  very  year  in  which 
it  did  actually  occur.  Now,  both  the  Lydians  and  the  Medes, 
when  they  saw  night  coming  on  instead  of  day,  ceased  from 
battle,  and  both  parties  were  more  eager  to  make  peace  with 
each  other." 

If,  in  this  case,  we  knew  when  and  where  the  battle  was 
fought,  and  if  we  knew  that  the  darkness  referred  to  was 
really  that  of  a  total  eclipse  of  the  sun,  it  would  be  easy  to 
compute  very  nearly  what  must  have  been  the  course  of  the 
moon  in  order  that  the  dark  shadow  might  have  passed  over 
the  field  of  battle.  But,  to  the  reader  who  reflects  upon  the 
uncritical  character  of  Herodotus,  the  vagueness  of  his  descrip- 
tion of  the  occuri-ence  will  suggest  some  suspicions  whether 
we  have  really  a  total  eclipse  to  deal  with.  Besides,  the  time 
when  the  battle  was  fought  is  doubtful  by  twenty  years  or 
more,  and  the  only  way  in  which  it  has  been  fixed  is  by  cal- 
culating from  the  tables  of  the  sun  and  moon  all  the  total 
eclipses  which  passed  over  the  region  in  which  the  battle  took 
place  between  the  admissible  limits  of  time.  Thus,  it  is  found 
that  the  only  date  which  will  fulfil  the  conditions  is  May  2Stli, 
B.C.  584,  when  there  must  have  been  a  total  eclipse  in  Asia 


100     SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

Minor  or  its  neighborhood.  But,  unless  we  suppose  that  it 
was  really  a  total  eclipse  which  caused  the  battle  to  cease, 
nothing  can  be  concluded  respecting  it ;  and  as  this  point 
seems  uncertain,  it  is  not  likely  that  astronomers  will  lay 
much  stress  upon  it. 

Another  celebrated  eclipse  of  the  sun  is  known  as  the 
eclipse  of  Agathocles.  The  fleet  of  this  commander,  beinj> 
blockaded  in  the  port  of  Syracuse  by  the  Carthaginians,  was 
enabled  to  escape  to  sea  at  a  moment  when  the  attention  of 
the  enemy  was  diverted  by  a  provision  convoy,  and  sailed  to 
make  a  descent  upon  Carthage.  "  The  next  day  there  was 
such  an  eclipse  of  the  sun  that  the  day  wholly  put  on  the 
appearance  of  night,  stai-s  being  seen  everywhere."  There  ie 
no  reasonable  doubt  that  this  was  a  total  eclipse  of  the  sun, 
and  the  date  is  well  established,  being  Auo-ust  14th,  b.c.  309. 
But,  unfortunately,  it  is  not  known  whether  Agathocles  went 
to  the  north  or  the  south  of  Sicily  in  his  passage  to  Car- 
thage, and  hence  we  cannot  obtain  any  certain  result  from 
this  eclipse. 

These  historical  accounts  of  total  eclipses  being  uncertain, 
an  attempt  has  been  made  to  derive  tlie  moon's  acceleration 
from  the  eclipses  of  the  moon  recorded  by  Ptolemy  in  the 
Almagest,  and  from  the  observations  of  the  Arabian  astrono- 
mers in  tlie  ninth  and  tenth  centuries.  These  observations 
agree  as  fairh'  as  could  be  expected  in  assigning  to  the  moon 
a  secular  acceleration  of  about  8".4,  a  little  more  than  2" 
greater  than  that  computed  from  gravitation.  On  the  other 
hand,  if  we  accept  the  eclipse  of  Thales  as  total  where  the 
battle  was  fought,  the  total  acceleration  will  be  about  12",  so 
that  the  two  results  are  entirely  incompatible.  The  question 
which  is  correct  must  be  decided  by  future  investigation;  but 
the  author  believes  the  smaller  value  to  be  founded  on  the 
more  trustworthy  data. 

The  secular  acceleration  is  not  the  only  variation  in  the 
moon's  mean  motion  which  has  perplexed  the  mathematicians. 
About  the  close  of  the  last  century,  it  was  found  by  Laplace 
that  the  moon  had,  for  a  number  of  yeai*s,  been  falling  behind 


INEQUALITIES  IN  THE  MOTION  OF  THE  MOON.         101 

ner  calculated  place,  a  result  which  seemed  to  show  that  there 
was  some  oscillation  of  long  period  which  had  been  overlooked. 
He  made  two  conjectural  explanations  of  this  inequality,  but 
both  were  disproved  by  subsequent  investigators.  The  ques- 
tion, therefore,  remained  without  any  satisfactory  solution  till 
1846,  when  Hansen  announced  that  the  attraction  of  Venus 
produced  two  inequalities  of  long  period  in  the  moon's  mo- 
tion, which  had  been  previously  overlooked,  and  that  these 
fully  accounted  for  the  observed  deviations  of  the  moon's  po- 
sition. These  terms  were  recomputed  by  Delaunay,  and  he 
found  for  one  of  them  a  result  agreeing  very  well  with  Han- 
sen's. But  the  second  came  out  so  small  that  it  could  never  be 
detected  from  observations,  so  that  here  was  another  mathe- 
matical discrepancy.  Tliere  was  not  room,  however,  for  much 
discussion  this  time.  Plansen  himself  admitted  that  he  had 
been  unal)le  to  determine  tlie  amount  of  this  inequality  in  a 
satisfactory  manner  from  the  theory  of  gravitation,  and  had 
therefore  made  it  agree  with  observation,  an  empirical  process 
which  a  matliematician  would  never  adopt  if  he  could  avoid 
it.  Even  if  observations  were  thus  satisfied,  doubt  would  still 
remain.  But  it  has  lately  been  found  that  this  empirical 
term  of  Hansen's  no  longer  agrees  with  observation,  and  that 
it  does  not  satisfactorily  agree  with  observations  before  1700. 
In  consequence,  there  are  still  slow  changes  in  the  motion  of 
our  satellite  which  gravitation  has  not  yet  accounted  for.  We 
are,  apparently,  forced  to  the  conclusion  either  that  the  iiiotion 
of  the  moon  is  influenced  by  some  other  cause  than  the  gravi- 
tation of  the  other  heavenly  bodies,  or  that  these  inequalities 
are  only  apparent,  being  really  due  to  small  changes  in  the 
earth's  axial  rotation,  and  in  the  consequent  length  of  the  day. 
If  we  admit  the  latter  explanation,  it  will  follow  that  tlie 
aarth^s  rotation  is  influenced  by  some  other  cause  than  the 
tidal  friction;  and  that,  instead  of  decreasing  uniformly,  it  va- 
ries from  time  to  time  in  an  irregular  manner.  The  observed 
inequalities  in  the  motion  of  the  moon  may  be  fully  accounted 
for  by  changes  in  the  earth's  rotation,  amounting  in  the  ag- 
gregate to  half  a  minute  or  so  of  time — changes  which  could 


102     SYSTEM  OF  THE  WOULD  HISTORICALLY  DEVELOPED. 

be  detected  by  a  perfect  clock  kept  going  for  a  number  of 
years.  But,  as  it  takes  many  years  for  these  changes  to  occur, 
no  clock  yet  made  will  detect  them. 

Yet  another  change  not  entirely  accounted  for  on  the  the- 
ory of  gravitation  occurs  in  the  motion  of  the  planet  Mercury. 
From  a  discussion  of  all  the  observed  transits  of  this  planet 
across  the  disk  of  the  sun,  Levei'rier  lias  found  that  the  mo- 
tion of  the  perihelion  of  Mercury  is  about  40  seconds  in  a 
century  greater  than  that  computed  from  the  gravitation  of 
the  other  planets.  This  he  attributes  to  the  action  of  a  gi-oup 
of  small  planets  between  Mercury  and  the  sun.  In  this  form, 
however,  the  explanation  is  not  entirely  satisfactory.  In  the 
first  place,  it  seems  hardly  possible  that  such  a  group  of  plan- 
ets could  exist  without  being  detected  during  total  eclipses  of 
the  sun,  if  not  at  other  times.  In  the  next  place,  granting 
them  to  exist,  they  must  produce  a  secular  variation  in  the 
position  of  the  orbit  of  Mercury,  whereas  this  variation  seems 
to  agree  exactly  with  theor}'.  Leverrier  explains  this  by  sup- 
posing the  group  of  asteroids  to  be  in  the  same  plane  with  the 
orbit  of  Mercury,  but  it  is  exceedingly  improbable  that  such 
a  group  would  be  found  in  this  plane.  There  is,  however,  an 
allied  explanation  which  is  at  least  worthy  of  consideration. 
The  phenomenon  of  the  zodiacal  light,  to  be  described  here- 
after, shows  that  there  is  an  immense  disk  of  matter  of  some 
kind  surrounding  the  sun,  and  extending  out  to  the  orbit  of 
the  earth,  where  it  gradually  fades  away.  The  nature  of  this 
matter  is  entirely  unknown,  but  it  may  consist  of  a  swarm  of 
minute  particles,  revolving  round  the  sun,  and  reflecting  its 
light,  like  planets.  If  the  total  mass  of  these  particles  is  equal 
to  that  of  a  very  small  planet,  say  a  tenth  the  mass  of  the 
earth,  it  would  cause  the  observed  motion  of  the  perihelion  of 
Mercury.  The  evidence  on  this  subject  will  be  considered 
more  fully  in  treating  of  Mercury. 

With  the  exceptions  just  described,  all  the  motions  in  the 
solar  system,  so  far  as  known,  agree  perfectly  with  the  i-esults 
of  the  theory  of  gravitation.  The  little  imperfections  which 
still  exist  in  the  astronomical  tables  seem  to  proceed  mainly 


RELATION  OF  THE  PLANETS  AND  STARS.  103 

from  errors  in  the  data  from  which  tlie  mathematician  must 
start  in  computing  the  motion  of  any  planet.  The  time  of 
revolution  of  a  planet,  the  eccentricity  of  its  orbit,  the  position 
of  its  perihelion,  and  its  place  in  the  orbit  at  a  given  time,  can 
none  of  them  be  computed  from  the  theory  of  gravitation,  but 
must  be  derived  from  observations  alone.  If  the  observations 
were  absolutely  perfect,  results  of  any  degree  of  accuracy 
could  be  obtained  from  them ;  but  the  imperfections  of  all 
instruments,  and  even  of  the  human  sight  itself,  prevent  ob- 
servations from  attaining  the  degree  of  precision  sought  after 
by  the  theoretical  asti'onomer,  and  make  the  considerations  of 
"errors  of  observation"  as  well  as  of  "errors  of  the  tables" 
constantly  necessary. 

§  7.  Relation  of  the  Planets  to  the  Stars. 

In  Chapter  I.,  §  3,  it  was  stated  that  the  heavenly  bodies 
belong  to  two  classes,  the  one  comprising  a  vast  multitude  of 
stars,  which  always  preserved  their  relative  positions,  as  if  they 
were  set  in  a  sphere  of  crystal,  while  the  others  moved,  each 
in  its  own  orbit,  according  to  laws  which  have  been  described. 
We  now  know  that  these  moving  bodies,  or  planets,  foi-m  a 
sort  of  family  by  themselves,  known  as  tlie  Solar  System. 
This  system  consists  of  the  sun  as  its  centre,  with  a  number  of 
primary  planets  revolving  around  it,  and  satellites,  or  second- 
ary planets,  revolving  around  them.  Before  the  invention  of 
the  telescope  but  six  primary  planets  were  known,  including 
the  earth,  and  one  satellite,  the  moon.  By  the  aid  of  tliat  in- 
strument, two  great  primary  planets,  outside  the  orbit  of  Sat- 
urn, and  an  immense  swarm  of  smaller  ones  between  the  oj*- 
bits  of  Mars  and  Jupiter,  have  been  discovered ;  Avhile  the 
four  outer  planets — Jupiter,  Saturn,  Uranus,  and  Neptune  — 
are  each  the  centre  of  motion  of  one  or  more  satellites.  The 
sun  is  distinguished  from  the  planets,  not  only  by  his  immense 
mass,  which  is  several  hundred  times  that  of  all  the  other  bod- 
ies of  his  system  combined,  but  by  the  fact  that  he  shines  by 
his  own  light,  while  the  planets  and  satellites  are  dark  bodies, 
shining  only  by  reflecting  the  lisht  of  the  sun. 
F 


104    SYSTEM  OF  THE  WORLD  HISTORICALLY  DEVELOPED. 

A  remarkable  symmetry  of  structure  is  seen  in  this  system, 
in  that  all  the  large  planets  and  all  the  satellites  revolve  in 
orbits  which  are  nearly  circular,  and,  the  satellites  of  the  two 
outer  planets  excepted,  nearly  in  the  same  plane.  This  family 
of  planets  are  all  bound  together,  and  kept  each  in  its  respec- 
tive orbit,  by  the  law  of  gravitation,  the  action  of  which  is  of 
such  a  nature  that  each  planet  may  make  countless  revolutions 
without  the  structure  of  the  system  undergoing  any  change. 

Turning  our  attention  from  this  system  to  the  thousands  of 
fixed  stare  which  stud  the  heavens,  the  first  thing  to  be  consid- 
ered is  their  enormous  distance  asunder,  compared  with  the 
dimensions  of  the  solar  system,  though  the  latter  are  them- 
selves inconceivably  great.  To  give  an  idea  of  the  relative 
distances,  suppose  a  voyager  through  tlie  celestial  spaces  could 
travel  from  the  sun  to  the  outermost  planet  of  our  system  in 
twenty-four  hours.  So  enormous  would  be  his  velocity,  that  it 
■would  carry  him  across  the  Atlantic  Ocean,  from  New  Tork 
to  Liverpool,  in  less  than  a  tenth  of  a  second  of  the  clock. 
Starting  from  the  sun  with  this  velocity,  he  would  cross  tlie 
orbits  of  the  inner  planets  in  rapid  succession,  and  the  outer 
ones  more  slowly,  until,  at  the  end  of  a  single  day.  he  would 
reach  the  confines  of  our  system,  crossing  the  orbit  of  Xeptune. 
But,  though  he  passed  eiglit  planets  the  first  day,  he  would 
pass  none  the  next,  for  he  would  have  to  journey  eighteen  or 
twenty  years,  without  diminution  of  speed,  before  he  would 
reach  the  nearest  star,  and  would  then  have  to  continue  his 
journey  as  far  again  befoi-e  he  could  reach  another.  All  the 
planets  of  our  system  would  have  vanished  in  the  distance,  in 
the  course  of  the  first  three  days,  and  the  sun  would  be  but  an 
insignificant  star  in  the  firmament.  The  conclusion  is,  that 
our  sun  is  one  of  an  enormous  number  of  self-luminous  bodies 
scattered  at  such  distances  that  yeai-s  would  be  required  to 
traverse  the  space  between  them,  even  when  the  voyager  went 
at  the  rate  we  liave  supposed.  The  solar  and  the  stellar  sys- 
tems thus  ofFer  us  two  distinct  fields  of  inquiry,  into  which  we 
shall  enter  after  describing  the  instruments  and  methods  by 
which  thev  are  investigated. 


PART  IL— PRACTICAL  ASTRONOMY, 


INTRODUCTORY  REMARKS. 

Should  the  reader  ask  what  Practical  Astronomy  is,  the 
best  answer  might  be  given  him  by  a  statement  of  one  of  its 
operations,  showing  how  eminently  practical  our  science  is. 
"Place  an  astronomer  on  board  a  ship;  blindfold  him  ;  carry 
him  by  any  route  to  any  ocean  on  the  globe,  whether  under 
the  tropics  or  in  one  of  the  frigid  zones ;  land  him  on  the 
wildest  rock  that  can  be  found;  remove  his  bandage, and  give 
him  a  chronometer  regulated  to  Greenwich  or  Washington 
time,  a  transit  instrument  with  the  proper  appliances,  and  the 
necessary  books  and  tables,  and  in  a  single  clear  night  he  can 
tell  his  position  within  a  hundred  yards  by  observations  of  the 
stars."  This,  from  a  utilitarian  point  of  view,  is  one  of  the 
most  important  operations  of  Practical  Astronomy.  When  we 
travel  into  regions  little  known,  whether  on  the  ocean  or  on 
the  Western  plains,  or  when  we  wish  to  make  a  map  of  a 
country,  we  have  no  way  of  finding  our  position  by  reference 
to  terrestrial  objects.  Our  only  course  is  to  observe  the  heav- 
ens, and  find  in  what  point  the  zenith  of  our  place  intersects 
the  celestial  sphere  at  some  moment  of  Greenwich  or  Wash- 
ington time,  and  then  the  problem  is  at  once  solved.  The  in- 
struments and  methods  by  which  this  is  done  may  also  be  ap- 
plied to  celestial  measurements,  and  thus  we  have  tlie  art  and 
science  of  Practical  Astronomy.  To  speak  more  generally, 
Practical  Astronomy  consists  in  the  description  and  investiga- 
tion of  the  instruments  and  methods  employed  by  astronomers 
in  the  work  of  exploring  and  measuring  the  heavens,  and  of 


lOQ  PRACTICAL   ASTRONOMY. 

determining  positions  on  the  earth  by  observations  of  the  heav- 
enly bodies.  The  general  construction  of  these  instruments, 
and  the  leading  principles  which  underlie  their  use  and  em- 
ployment, can  be  explained  ■with  the  aid  of  a  few  technical 
terms  which  we  shall  define  as  we  have  occasion  for  them. 

The  instruments  employed  by  the  ancients  in  celestial  ob- 
servations were  so  few  and  simple  that  we  may  dispose  of 
them  very  briefly.  The  only  ones  we  need  mention  at  pres- 
ent are  the  gnomon  and  the  astrolabe,  or  armillary  sphere. 
The  former  was  little  more  than  a  large  sun-dial  of  the  sim- 
plest construction,  by  which  the  altitude  and  position  of  the 
snn  were  determined  from  the  length  and  direction  of  the 
shadow  of  an  upright  pillar.  If  the  sun  wei-e  a  point  to  the 
sight,  this  method  would  admit  of  considerable  accuracy,  be- 
cause the  shadow  would  then  be  sharply  defined.  In  fact, 
however,  owing  to  the  apparent  size  of  the  solar  disk,  the  shad- 
ow of  any  object  at  the  distance  of  a  few  feet  becomes  ill-de- 
fined, shading  off  so  gradually  that  it  is  hard  to  say  where  it 
ends.  No  approach  to  accuracy  can  therefore  be  attained  by 
the  ffnomon. 

Notwithstanding  the  rudeness  of  this  instrument,  it  seems 
to  have  been  the  one  universally  employed  by  the  ancients 
for  the  determination  of  the  times  when  the  sun  reached 
the  equinoxes  and  solstices.  The  day  when  the  shadow  was 
shortest  marked  the  summer  solstice,  and  a  comparison  of 
the  length  of  the  shadow  with  the  height  of  the  style  gave, 
by  a  trigonometric  calculation,  the  altitude  of  the  sun.  The 
day  when  the  shadow  was  longest  marked  the  winter  solstice ; 
and  the  day  when  the  altitude  of  the  sun  was  midway  between 
the  altitudes  at  the  two  solstices  marked  the  equinoxes.  Thus 
this  rude  instrument  served  the  purpose  of  determining  the 
length  of  the  year  with  an  accuracy  sufiicient  for  the  purposes 
of  daily  life.  But  so  immensely  superior  are  our  modern 
methods  in  accuracy,  that  the  astronomer  can  to-day  compute 
the  position  of  the  sun  at  any  hour  of  any  day  2000  years  ago 
with  far  greater  accuracy  than  it  could  have  been  observed 
with  a  gnomon. 


INTRODUCTORY  REMARKS. 


107 


The  armillaiy  sphere  consisted  of  a  combination  of  three 
circles,  one  of  which  could  be  set  in  the  plane  of  the  equator 
or  the  ecliptic;  that  is,  an  arm  moving  around  this  circle 
would  always  point  towards  some  part  of  the  equator  or  the 
ecliptic,  according  to  tlie  way  the  instrument  was  set.  The 
circle  in  question,  being  divided  into  degrees,  served  the  pur- 
pose of  measuring  the  angular  distance  of  any  two  bodies  in 
or  near  the  ecliptic,  as  the  sun  and  moon,  or  a  star  and  planet. 
It  was  by  such  measures  that  Hipparchns  and  Ptolemy  were 
able  to  determine  the  larger  inequalities  in  the  motions  of  the 
eun,  moon,  and  planets. 


E     A. 


Pig.  27.— Armillary  sphere,  as  described  by  Ptolemy,  and  used  by  him  and  by  Hipparchns. 
The  circle  EI  is  set  in  the  plane  of  the  ecliptic,  the  line  PP  being  directed  towards  its 
pole.  The  circle  ApMp  passes  throngh  the  poles  of  both  the  ecliptic  and  tlie  equator. 
The  inner  pair  of  circles  turn  on  the  axis  PP,  and  are  furnished  with  sights  which  may 
be  directed  on  the  object  to  bO  observed.  The  latitude  and  longitude  of  the  object  are 
then  read  off  by  the  position  of  the  circles. 


108  PRACTICAL  ASTRONOMY. 


CHAPTER  I. 

THE     TELESCOPE. 

§  1.   The  First  Telescopes. 

The  telescope  is  so  essential  a  part  of  every  instrnraent  in- 
tended for  astronomical  measurement,  that,  apart  from  its  own 
importance,  it  must  claim  tlie  lirst  place  in  any  description  of 
astronomical  instruments.  The  question.  Who  made  the  first 
telescope  ?  was  long  discussed,  and,  perhaps,  will  never  be  con- 
clusively settled.  If  the  question  were  merely,  Who  is  entitled 
to  the  credit  of  the  invention  under  the  rules  according  to 
which  scientific  credit  is  now  awarded  ?  we  conceive  that  the 
answer  must  be,  Galileo.  The  first  publisher  of  a  result  or 
discovery,  supposing  such  result  or  discovery  to  be  honestly 
his  own,  now  takes  the  place  of  the  first  inventor ;  and  there 
is  little  doubt  that  Galileo  was  the  first  one  to  show  the  world 
how  to  make  a  telescope.  But  Galileo  himself  says  that  it 
was  through  hearing  that  some  one  in  France  or  Holland  had 
made  an  instrument  which  magnified  distant  objects,  and 
brought  them  nearer  to  the  view,  that  he  was  led  to  inquire 
how  such  a  result  could  be  reached.  He  seems  to  have  ob- 
tained from  others  the  idea  that  the  instrument  was  possible, 
but  no  hint  as  to  how  it  was  made. 

As  a  historic  fact,  however,  there  is  no  serious  question  that 
the  telescope  originated  in  Holland ;  but  the  desire  of  the  in- 
ventors, or  of  the  authorities,  or  both,  to  profit  by  the  posses- 
sion of  an  instrument  of  such  extraordinary  powers,  prevented 
the  knowledge  of  its  construction  from  spreading  abroad.  The 
honor  of  being  the  originator  has  been  claimed  for  three  men, 
each  of  whom  has  had  his  partisans.    Their  names  are  Metius, 


THE  FIRST  TELESCOPES.  109 

Lipperhey,  and  Jansen ;  the  last  two  being  spectacle-makers 
in  the  town  of  Middleburg,  and  the  first  a  professor  of  mathe- 
matics. 

The  claims  of  Jansen  were  sustained  by  Peter  Borelli,  au- 
thor of  a  small  book*  on  the  subject,  and  on  the  strength  of 
his  authority  Jansen  was  long  held  to  be  the  true  inventor. 
His  story  was  that  Jansen  had  shown  a  telescope  sixteen  inches 
long  to  Prince  Maurice  and  the  Archduke  Albert,  who,  per- 
ceiving the  importance  of  the  invention  in  war,  offered  him 
money  to  keep  it  a  secret.  If  this  story  be  true,  it  would  be 
interesting  to  know  on  what  terms  Jansen  was  induced  to  sell 
out  his  right  to  immortality.  But  Borelli's  case  rests  on  tlie 
testimony  of  two  or  three  old  men  who  had  known  Jansen  in 
their  youth,  taken  forty-five  or  fifty  years  after  the  occurrence 
of  the  events,  when  Jansen  had  long  been  dead,  and  has  there- 
fore never  been  considered  as  fully  proved. 

About  1830,  documentary  evidence  was  discovered  which 
showed  that  Ilans  Lipperhej',  whom  Borelli  claims  to  have 
been  a  second  inventor  of  the  telescope,  made  application  to 
the  States-general  of  Holland,  on  November  2d,  1608,  for  a 
patent  for  an  instrument  to  see  with  at  a  distance.  About 
the  same  time  a  similar  application  was  made  by  James  Me- 
tius.  The  Government  refused  a  patent  to  Lipperhey,  on  the 
ground  that  the  invention  was  already  known  elsewhere,  but 
ordered  several  instruments  from  him,  and  enjoined  him  to 
keep  their  construction  a  secret. 

It  will  be  seen  from  this  that  the  historic  question.  Who 
made  the  first  telescope?  does  not  admit  of  being  easily  an- 
swered ;  but  that  tlie  powers  of  the  instrument  were  well 
known  in  Holland  in  1608  seems  to  be  shown  by  the  i-efusal 
of  a  patent  to  Lipperhey.  The  efforts  made  in  that  country 
to  keep  the  knowledge  of  the  construction  a  secret  were  so 
far  successful  that  we  mxust  go  from  Holland  to  Italy  to  find 
how  that  knowledge  first  became  public  property.  About  six 
months  after  the  petitions  of  Lipperhey  and  Metius,  Galileo 

*  "  De  Vero  Telescopii  Inventore,''  The  Hngiie,  1655. 


XIO  PRACTICAL  ASTRONOMY. 

was  in  Venice  on  a  visit,  and  there  received  a  letter  from 
Paris,  in  which  the  invention  was  mentioned.  He  at  once  set 
himself  to  the  reinvention  of  the  instrument,  and  was  so  suc- 
cessful that  in  a  few  days  he  exhibited  a  telescope  magnify- 
ing three  times,  to  the  astonished  authorities  of  the  city.  Re- 
turning to  his  home  in  Florence,  he  made  other  and  larger 
ones,  W'hich  revealed  to  him  the  spots  on  the  sun,  the  phases 
of  Yenus,  the  mountains  on  the  moon,  the  satellites  of  Jupiter, 
the  seeming  handles  of  Saturn,  and  some  of  the  myriads  of 
stars,  separately  invisible  to  the  naked  eye,  whose  combined 
^ight  forms  the  milky-way.  But  the  laigest  of  these  instru- 
ments magnified  only  about  thirty  times,  and  was  so  imper- 
fect in  construction  as  to  be  far  from  showing  as  much  as 
could  be  seen  with  a  modern  telescope  of  that  power.  The 
Galilean  telescope  was,  in  fact,  of  the  simplest  construction, 
consisting  of  the  combination  of  a  pair  of  lenses,  of  whicli  the 
larger  was  convex  and  the  smaller  concaxe,  as  shown  in  the 
following  figure : 


B 
Fia.  28.— The  Galilean  telescope.    The  dotted  lines  show  the  course  of  the  rays  through 

the  leuses. 

The  distance  of  the  lenses  was  snch  that  the  rays  of  light 
from  a  star  passing  through  the  large  convex  lens,  or  object- 
glass,  OB,  met  the  concave  lens,  R,  before  reaching  the  focus. 
The  position  of  this  concave  lens  was  such  that  the  rays 
should  emerge  from  it  nearly  parallel.  This  form  of  tele- 
scope is  still  used  in  opera -glasses,  because  it  can  be  made 
shorter  than  any  other. 

The  improvements  in  the  telescope  since  Galileo  can  be 
best  understood  if  we  give  a  brief  statement  of  the  princi- 
ples on  which  all  modern  telescopes  are  constructed.  The 
properties  of  every  such  instrument  depend  on  the  power  pos- 
sessed by  a  lens  or  by  a  concave  mirror  of  forming  an  im- 
age of  any  distant  object  in  its  focus.     This  is  done  in  the 


THE  FIRST  TELESCOPES.  HI 

case  of  the  lens  by  refracting  the  light  whicli  passes  through 
it,  and  in  the  case  of  the  mirror  by  reflecting  back  tlie  rays 
which  strike  it.  In  order  to  form  an  image  of  a  point,  it  is 
necessary  that  a  portion  of  the  rays  of  light  which  emanate 
from  the  point  shall  be  collected  and  made  to  converge  to 
some  other  point.     For  instance,  in  the  following  ligure,  the 


i>2»;>     •>  ^  "      ~^- — .___  ji' 


E 


Fio.  29.— Formatiou  of  au  image  by  a  leus. 


nearly  parallel  rays  emanating  from  a  distant  point  in  the  di- 
rection from  which  the  arrow  is  coming  strike  the  lens,  Z, 
and  as  they  pass  through  it  are  bent  out  of  tlieir  course,  and 
made  to  converge  to  a  point,  F.  Continuing  their  course, 
they  diverge  from  F  exactly  as  if  F  itself  were  a  luminous  point, 
a  cone  of  light  being  formed  with  its  apex  at  F.  An  observer 
placing  his  eye  witliin  this  cone  of  rays,  and  looking  at  F, 
will  tliere  seem  to  see  a  shining  point,  although  really  there 
is  nothing  there.  This  apparent  shining  point  is,  in  the  lan- 
guage of  astronomy,  called  the  image  of  the  real  point.  The  dis- 
tance, OF,  is  called  the  focal  length  of  the  lens. 

If,  instead  of  a  simple  point,  we  have  an  object  of  some 
apparent  magnitude,  as  the  moon,  a  house,  or  a  tree,  then  the 
light  from  each  point  of  the  object  will  be  brought  to  a  cor- 
responding point  near  F.  To  find  where  this  corresponding 
point  is,  we  have  only  to  draw  a  line  from  each  point  of  an 
object  through  the  centre  of  the  lens,  and  continue  it  as  far  as 
the  focus.  Each  point  of  the  object  will  then  have  its  own 
point  in  the  image.  These  points,  or  images,  will  be  spread 
out  over  the  surface,  EFE,  which  is  called  the  focal  plane,  and 
will  make  up  a  representation,  or  image,  of  the  entire  object 
on  a  small  scale,  but  in  a  reversed  position,  exactly  as  in  the 
camera  of  a  photographer.  An  eye  at  B  within  the  cone  of 
rays  will  then  see  all  or  a  part  of  the  object  reversed  in  the 
focal  plane.     The  image  thus  formed  may  be  viewed  by  the 


112  PRACTICAL  ASTRONOMY. 

eye  as  if  it  were  a  real  object;  and  as  a  minute  object  may  be 
viewed  by  a  magnifying  lens,  so  such  a  lens  may  be  used  to 
view  and  magnify  the  image  formed  in  the  focal  plane.  In 
the  large  lens  of  long  focus  to  form  the  image  in  the  focal 
plane,  and  the  small  lens  to  view  and  magnify  this  image,  we 
have  the  two  essential  parts  of  a  refracting  telescope.  The 
former  lens  is  called  the  objective,  or  object-glass,  and  the  latter 
the  eye-piece,  eye-lens,  or  ocular. 

The  magnifying  power  of  a  telescope  depends  upon  the  rel- 
ative focal  lengths  of  the  objective  and  ocular.  The  greater 
the  focal  length  of  the  former — that  is,  the  greater  the  distance 
OF — the  larger  the  image  will  be ;  and  tlie  less  the  focal  length 
of  the  eye-lens,  the  nearer  the  eye  can  be  brought  to  the  im- 
age, and  the  more  the  latter  will  be  magnified.  The  magnify- 
ing power  is  found  by  dividing  tlie  focal  length  of  the  objec- 
tive by  that  of  the  eye-lens.  For  instance,  if  the  focal  length 
of  an  objective  were  36  inches,  and  that  of  the  eye-lens  were 
three-quarters  of  an  inch,  the  quotient  of  these  numbers  would 
be  48,  wliicli  would  be  the  magnifying  power.  If  the  focal 
lengths  of  these  lenses  were  equal,  the  telescope  would  not 
magnify  at  all.  B}'  simply  turning  a  telescope  end  for  end, 
aiid  looking  in  at  the  objective,  we  have  a  reversed  telescope, 
w^liich  diminishes  objects  in  the  same  proportion  that  it  mag- 
nifies them  when  not  reversed. 

From  the  foregoing  rule  it  follows  that  w^e  can,  theoretical- 
ly,  make  any  telescope  magnify  as  much  as  we  please,  by  sim- 
ply using  a  sufficiently  small  eye -lens.  If,  for  instance,  we 
wish  our  telescope  of  36  inches  focal  length  to  magnify  3600 
times,  we  have  only  to  apply  to  it  an  eye-lens  of  ^J-jj  of  an  inch 
focal  length.  But,  in  attempting  to  do  this,  a  difficulty  arises 
with  Avhich  astronomers  have  always  had  to  contend,  and 
which  has  its  origin  in  the  imperfection  of  the  image  formed 
by  the  object-glass."  No  lens  will  bring  all  the  rays  of  light 
to  absolutely  the  same  focus.  When  light  passes  throngh  a 
prism,  the  various  colors  are  refracted  unequal!}',  red  being 
refracted  tlie  least,  and  violet  the  most.  It  is  the  same 
when  light  is  refracted  by  a  lens,  and  the  consequence  is  that 


THE  FIRST  TELESCOPES.  115 

the  red  rays  will  be  brought  to  the  farthest  focus,  and  the  vio- 
let to  the  nearest,  while  the  intermediate  colors  will  be  scat- 
tered between.  As  all  the  light  is  not  brought  to  the  same 
focus,  it  is  impossible  to  get  any  accurate  image  of  a  star  or 
other  object  at  which  the  telescope  is  pointed,  the  eye  seeing 
only  a  confused  mixture  of  images  of  various  colors.  When 
ft  sufficiently  low  magnifying  power  is  used,  the  confusion  will 
be  slight,  the  edges  of  the  object  being  indistinct,  and  made 
lip  of  colored  fringes.  When  the  magnifying  power  is  in- 
creased, the  object  will  indeed  look  larger,  but  these  confused 
fringes  will  look  larger  in  the  same  proportion  ;  so  that  the 
observer  will  see  no  more  tlian  before.  This  separation  of  the 
light  in  a  telescope  is  termed  chromatic  aberration. 

Such  was  the  difficulty  which  the  successors  of  Galileo  en- 
countered in  attempting  to  improve  the  telescope,  and  which 
they  found  it  impossible  to  obviate.  They  found,  however, 
that  they  could  diminish  it  by  increasing  the  length  of  the  tel- 
escope, and  the  consequent  size  of  the  confused  image.  If 
they  made  an  object-glass  of  any  fixed  diameter,  say  six  inches, 
they  found  that  the  image  M^as  no  more  confused  when  the 
focal  length  was  sixty  feet  than  when  it  was  six,  and  tlie  same 
eye-lens  could  therefore  be  used  in  both  cases.  But  the  im- 
ase  in  the  focus  of  the  first  was  ten  times  as  large  as  in  the 
second,  and  thus  using  the  same  eye-lens  would  give  ten  times 
the  magnifying  power.  Iluyghens,  Cassini,  Hevelius,  and  oth- 
er astronomers  of  the  latter  part  of  the  seventeenth  century, 
made  telescopes  a  hundred  feet  or  upwards  in  length.  Some 
astronomers  then  had  to  dispense  with  a  tube  entirely  ;  the  ob- 
jective being  mounted  by  Cassini  on  the  top  of  a  long  pole, 
while  the  ocular  was  moved  along  near  the  ground.  Hevelius 
kept  his  objective  and  ocular  connected  by  a  long  rod  which 
replaced  the  tube.  Very  complicated  and  ingenious  arrange- 
ments were  sometimes  used  in  managing  these  huge  instru- 
ments, of  which  we  give  one  specimen,  taken  from  the  work 
of  Blanchini,"^e52Jen  et  Phosphori  Nova  Pha^noinena"  in  which 
that  astronomer  describes  his  celebrated  observations  on  the 
rotation  of  Venus. 


116  PRACTICAL  ASTRONOMY. 

§  2.  The  Achromatic  Telescope. 

A  century  and  a  half  elapsed  from  the  time  when  Galileo 
showed  his  first  telescope  to  the  authorities  of  Venice  before 
any  method  of  destroying  the  chromatic  aberration  of  a  lens 
was  discovered.  It  is  to  Dollond,  an  English  optician,  that  the 
practical  construction  of  the  achromatic  telescope  is  due,  al- 
though the  principle  on  which  it  depends  was  firet  published 
by  Euler,  the  German  mathematician.  The  invention  of  Dol- 
lond  consists  in  the  combination  of  a  convex  and  concave  lens 
of  two  kinds  of  glass  in  such  a  way  that  their  aberrations 
shall  counteract  each  other.  How  this  is  effected  will  be  best 
seen  by  taking  the  case  of  refraction  by  a  prism,  where  the 
same  principle  comes  into  play.  The  separation  of  the  light 
into  its  prismatic  colors  is  here  termed  dispersion.  Suppose, 
now,  that  we  take  two  prisms  of  glass,  ABC  and  A  CD,  (Fig. 
31),  and  join  them  in  the  manner  shown  in  the  figure.     If  a 


£  c 

FiQ.  31.— Refraction  through  a  componnd  prism. 

ray,  RS,  pass  througli  the  two,  their  actions  on  it  will  tend 
to  counteract  each  other,  owing  to  the  opposite  directions  in 
which  their  angles  are  turned,  and  the  ray  will  be  refracted 
only  by  the  difference  of  the  refractive  powers,  and  dispersed 
by  the  difference  of  the  dispei*sive  powers.  If  the  dispersive 
powers  are  equal,  there  will  be  no  dispersion  at  all,  the  ray 
passing  through  without  any  separation  of  its  colors.  If  the 
two  prisms  are  made  of  the  sam.e  kind  of  glass,  their  dispersive 
powers  can  be  made  equal  only  by  making  them  of  the  same 
angle,  and  then  their  refractive  powei-s  will  be  equal  also,  and 
the  ray  will  pass  through  without  any  refraction.     As  our  ob- 


THE  ACHROMATIC  TELESCOPE.  117 

ject  is  to  have  refraction  without  dispersion,  a  combination  of 
prisms  of  the  same  kind  of  glass  cannot  effect  it. 

The  problem  which  is  now  presented  to  us  is,  Can  we  make 
two  prisms  of  different  kinds  of  glass  such  that  their  disper- 
sive powers  shall  be  equal,  but  their  refi-active  powers  un- 
equal? The  researches  of  Euler  and  Dollond  answered  this 
question  in  the  afhrmative  by  showing  that  the  dispersive 
power  of  dense  flint-glass  is  double  that  of  crown-glass,  while 
its  refractive  power  is  nearly  the  same.  Consequently,  if  we 
make  the  prism  ABC  of  crown  glass,  and  the  prism  ACD  of 
flint,  the  angle  of  the  flint  at  C  being  half  that  of  the  crown 
at  A,  the  two  opposite  dispersions  will  neutralize  each  other, 
and  the  rays  will  pass  through  without  being  broken  up  into 
the  separate  colors.  But  the  crown  prism,  with  double  the  an- 
gle, will  have  a  more  powerful  refractive  power  than  the  flint ; 
so  that,  by  combining  the  two,  we  shall  have  refraction  without 
dispersion^  which  solves  the  problem. 

The  manner  in  which  this  principle  is  applied  to  the  con- 
struction of  an  object-glass  is  this :  a  convex  lens  of  crown  is 
combined  with  a  concave  lens  of  flint  of  about  half  the  cur- 
vature. No  exact  rule  respecting  the  ratio  of  the  two  curva- 
tures can  be  given,  because  the  refractive  powers  of  different 
specimens  of  glass  differ  greatly,  and  the  proper  ratio  must, 
therefore,  be  found  by  trial  in  each  case.  Having  found  it, 
the  two  lenses  will  then  have  equal  aberrations,  but  in  oppo- 
site directions,  while  the  crown  refracting  more  powerfully 
•  than  the  flint,  the  rays  will  be  brought  to  a  focus  at  a  dis- 
tance a  little  more  than  double  the  focal  distance  of  the  former. 
A  combination  of  this  sort  is  called  an  achromatic  objective. 
Some  of  the  earlier  achromatic  objectives  were  made  of  three 
lenses,  a  double  concave  lens  of  flint  glass  being  fitted  be- 
tween two  double  convex  ones  of  crown.  At  present,  how- 
ever, but  two  lenses  are  used,  the  forms  of 
which,  as  used  in  the  smaller  European  tele-    i 

pcopes,  and  in  all  the  telescopes  of  Mr.  Alvan    ^'-— -___ 

Clark,  are  shown  in  Fi":.  32.     The  crown-    „       """;    . 

'  ~  Fig.  32.— Section  of  an 

glass  is  here  a  double  convex  lens,  and  the    achromatic  objective. 


lis  PRACTICAL  ASTROXOMT. 

curvatures  of  the  two  faces  are  equal.  The  curvature  of  the 
iuside  face  of  the  flint  is  the  same  as  that  of  the  crown,  so 
that  the  two  faces  fit  accurately  together,  while  the  outer  face 
is  nearly  flat.  If  the  dispersive  power  of  the  flint  were  just 
double  that  of  the  crown,  this  face  would  have  to  be  flat 
to  produce  achromatism ;  but  this  is  not  generally  the  case. 
The  fact  is  that,  as  no  two  specimens  of  glass  made  at  dif- 
ferent meltings  have  exactly  the  same  refractive  and  disper- 
sive powers,  the  optician,  in  making  a  telescope,  must  find  the 
ratios  of  dispersion  of  his  two  glasses,  and  then  give  the  outer 
face  of  his  flint  such  a  degree  of  curvature  as  to  neutralize 
the  dispersion  of  his  crown  glass.  Usually,  this  face  will  have 
to  be  slightly  concave. 

When  tlie  inner  faces  of  the  glasses  are  thus  made  to  fit,  it 
is  not  uncommon  to  join  the  glasses  together  with  a  transpar- 
ent balsam,  in  order  to  diminish  the  loss  of  light  in  passing 
through  the  glass.  "Whenever  light  falls  upon  transparent 
glass,  between  three  and  four  per  cent,  of  it  is  reflected  back, 
and  when,  after  passing  through,  it  leaves  again,  about  the 
same  amount  is  reflected  back  into  the  glass.  Consequently, 
about  seven  per  cent,  of  the  light  is  lost  in  passing  through 
each  lens.  But  when  the  two  lenses  are  joined  with  balsam 
or  castor-oil,  the  reflection  from  the  second  surface  of  the  flint 
and  the  first  surface  of  the  crown  is  greatly  diminished,  and  a 
loss  of  perhaps  six  per  cent,  of  the  light  is  avoided.* 

As  larger  and  more  perfect  achromatic  telescopes  were 
made,  a  new  source  of  aberration  was  discovered,  no  practical 
method  of  correcting  which  is  yet  known.  It  arises  from  the 
fact  that  flint  glass,  as  compared  with  crown,  disperses  the  blue 
^nd  of  the  spectrum  more  than  the  red  end.     If  we  make 


*  When  there  is  no  bals.atn,  .another  inconvenience  sometimes  arises  from  a 
Gouble  reflection  of  light  from  the  inner  surfaces  of  the  glass.  Of  the  light  re- 
flected back  from  the  first  surface  of  the  crown,  four  per  cent,  is  again  reflected 
from  the  second  surface  of  the  flint,  and  sent  down  to  the  focus  of  the  telescope 
with  the  direct  rays.  If  there  be  the  slightest  misplacement  of  one  of  the  lenses, 
the  reflected  rays  will  come  to  a  difl^'erent  focus  from  the  direct  ones,  and  everj 
bright  star  will  seem  to  have  a  small  companion  star  along-side  of  it. 


THE  ACHROMATIC  TELESCOPE.  119 

lenses  of  flint  and  crown  having  equal  dispersive  power,  we 
shall  find  that  the  red  end  is  longest  in  the  crown-glass  spec- 
trum, and  the  blue  end  in  the  flint-glass  spectrum.  The  con- 
sequence is  that  when  we  join  a  pair  of  prisms  in  reversed 
positions,  as  shown  in  Fig.  31,  the  two  dispersions  cannot  be 
made  to  destroy  each  other  entirely.  Instead  of  the  refracted 
light  being  all  joined  in  one  white  ray,  the  spectrum  will  be 
folded  over,  as  it  were,  the  red  and  indigo  ends  being  joined 
together,  the  faint  violet  light  extending  out  by  itself,  while 
the  yellow  and  green  are  joined  at  the  opposite  end.  This 
end  will,  therefore,  be  of  a  yellowish  green,  while  the  other 
end  is  purple. 

The  spectrum  tlms  formed  by  the  combination  of  a  flint 
and  c]'own  prism  is  termed  the  secondary  spectrum.  It  is  very 
much  shorter  than  the  oidinary  spectra  formed  by  either  the 
crown  or  the  flint  glass,  and  a  large  portion  of  the  light  is  con- 
densed near  the  yellowish-green  end.  The  effect  of  it  is  that 
the  refracting  telescope  is  not  jDcrfectly  achromatic,  though 
very  nearly  so.  In  a  small  telescope  the  defect  is  hardly  no- 
ticeable, the  only  drawback  being  that  a  bright  star  or  other 
object  is  seen  surrounded  by  a  blue  or  violet  areole,  formed  by 
the  indigo  rays  thrown  out  by  the  flint-glass.  If  the  eye-piece 
is  pushed  in,  so  that  the  star  is  seen,  not  as  a  point,  but  as  a 
small  disk,  the  centre  of  this  disk  will  be  gi'een  or  yellow, 
while  the  border  will  be  reddish  purple.  But,  in  the  immense 
refractors  of  two-feet  aperture  or  upwards,  of  which  a  number 
have  been  produced  of  late  years,  the  secondary  aberration 
constitutes  the  most  serious  optical  defect;  and  it  is  a  defect 
which,  arising  from  the  properties  of  glass  itself,  no  art  can 
diminish.  The  difliculty  may  be  lessened  in  the  same  way 
that  the  chromatic  aberration  was  lessened  in  the  older  tele- 
scopes, namely,  by  increasing  the  length  of  the  instrument. 
In  doing  this,  however,  with  glasses  of  such  large  size,  engi- 
neering difficulties  are  encountered  which  soon  become  insur- 
mountable. We  must,  therefore,  consider  that,  in  the  great 
refractors  of  recent  times,  the  limit  of  optical  power  for  such 
instruments  has  been  very  nearly  attained. 


120  FEACTICAL  ASTRONOMY, 

The  eye-piece  of  a  telescope,  as  well  as  its  objective,  con- 
sists of  two  glasses.  A  single  lens  will,  indeed,  answer  all 
the  purposes  of  seeing  an  object  in  the  centre  of  tlie  tield 
of  view,  but  the  field  itself  will  be  narrow  and  indistinct  at 
the  edges.  An  additional  lens,  term- 
ed the  tield -lens,  is  therefore  placed 
j^    B  M    very  near  the  image,  for  the  purpose 

*^'    g7?  F^    Qf  refracting  the  outer  rays  into  the 

proper  direction  to  form  a  distinct 
imaire  with  the  aid  of  the  eye- lens. 
^"^  ""l!:^:^'-"'"  I"  Fife'-  33  such  an  eve- piece  is  .-e^ 
resented,  in  which  the  tield- lens  is 
between  the  image  and  the  eye.  This  is  called  a  ;positive 
eye-piece.  In  the  negative  eye -piece  the  rays  pass  through 
the  tield-lens  just  before  coming  to  a  focus,  so  that  the  image 
is  formed  just  within  that  lens.  The  positive  eye -piece  is 
used  when  it  is  required  to  use  a  micrometer  in  the  focal 
plane  ;  but  for  mere  looking  the  negative  ocular  is  best.  All 
telescopes  are  supplied  with  a  number  of  eye -pieces,  by 
changing  which  the  magnifying  power  may  be  altered  to  suit 
the  observer. 

The  astronomical  telescope  used  with  these  eye-pieces  al- 
ways shows  objects  upside  down  and  right  side  left.  This 
causes  no  inconvenience  in  celestial  observations.  But  for 
viewing  terrestrial  objects  the  eye-piece  must  have  two  pairs 
of  lenses,  the  first  of  which  forms  a  new  image  of  the  object 
restored  to  its  proper  position,  which  image  is  viewed  by  the 
eye -piece  formed  of  the  second  pair.  This  combination  is 
called  an  erecting  or  terrestrial  eye-piece. 

§  3.  The  Mounting  of  the  Telescope. 

If  the  earth  did  not  revolve,  so  that  each  heavenly  body 
would  be  seen  hour  after  hour  and  day  after  da}'  in  nearly 
the  same  direction,  the  problem  of  using  great  telescopes 
would  be  much  simplified.  The  objective  and  the  eye-piece 
could  be  fixed  so  as  to  point  at  the  object,  and  the  observer 
could  scrutinize  it  at  his  leisure.     But  actually,  when  we  use 


THE  MOUNTING   OF  THE  TELESCOPE. 


121 


a  telescope,  the  diurnal  revolution  of  the  earth  is  apparently 
increased  in  proportion  to  tlie  magnifying  power  of  the  in- 
strument ;  and  if  the  latter  is  fixed,  and  a  high  power  is  used, 
the  object  passes  by  with  such  rapidity  that  it  is  impossible  to 
scrutinize  it.  Merely  to  point  a  telescope  at  an  object  needs 
many  special  contrivances,  because,  unless  the  pointing  is  ac- 
curate, the  object  cannot  be  found  at  all.  With  a  telescope, 
and  nothing  more,  an  observer  might  spend  half  an  hour  in 
vain  efforts  to  point  it  at  Sirius  so  accurately  that  the  image 
of  the  star  should  be  brought  into  the  field  of  view ;  and  then, 
before  he  got  one  good  look,  it  might  flit  away  and  be  lost 
again.  If  this  is  the  case  with  a  bright  star,  how  much  liarder 
must  it  be  to  point  at  the  planet  Neptune,  an  object  invisible 
to  the  naked  eye,  which  is  not  in  the  same  direction  two  min- 
utes in  succession !  It  will  readily  be  understood  that,  to  make 
any  astronomical  use  of  a  large  telescope,  two  things  are  abso- 
lutely necessary :  fii-st,  the  means  of  pointing  the  telescope  at 
any  object,  visible  or  invisible ;  and,  second,  the  means  of  mov- 
ing the  telescope  so  that 
it  sliall  follow  the  object 
in  its  diurnal  motion, 
and  thus  keep  its  image 
in  the  field  of  view.  The 
following  are  the  me- 
chanical contrivances  by 
which  these  objects  are 
effected : 

The  object-glass  is 
placed  in  one  end  of  a 
tube,  OF,  the  length  of 
the  tube  being  nearly 
equal  to  tlie  focal  length 
of  the  objective.  The 
eye-piece  is  fitted  into  a 
projection  at  the  lower 
end  of  the  tube,  K    The 

,  .  p     ,  V       •     i      F'o.  34 Mode  of  monnting  a  telescope  so  as  to  fol- 

Object  or  the    tube    is  to  low  a  star  in  its  dlurual  motion. 


122  PRACTICAL  ASTRONOMY. 

keep  tlie  glasses  in  their  proper  relative  positions,  and  to  pro- 
tect the  eye  of  the  observer  from  stray  light. 

The  tube  has  an  axis,  AB.,  tirmly  fastened  to  it  at  A  near  its 
middle,  which  axis  passes  through  a  cylindrical  case,  C,  into 
which  it  neatly  fits,  and  in  which  it  can  turn.  By  turning  the 
telescope  on  this  axis,  the  end  E  can  be  brought  towards  the 
reader,  and  0  from  him,  or  vice  versa.  This  axis  is  called  the 
declination  axis.  The  case,  C^  is  firmly  fastened  to  a  second 
axis,  DE,  supported  at  D  and  E  called  the  polar  axis.  This 
axis  points  to  the  pole  of  the  heavens,  and,  by  turning  it,  the 
whole  telescope,  with  the  part,  >4(7,  of  the  case,  may  be  brought 
towards  the  observer,  while  the  end  B  will  recede  from  him, 
or  vice  versa.  In  order  that  the  weight  of  the  telescope  may 
not  make  it  turn  on  the  polar  axis,  it  is  balanced  by  a  weight 
at  B,  on  the  other  end  of  the  declination  axis.  This  weight 
is  commonly  divided,  a  part  being  carried  by  the  axis,  and  a 
part  by  the  case,  C.  The  polar  axis  is  carried  by  a  frame,  F, 
well  fastened  on  top  of  a  pier  of  masonry. 

Such  is  the  general  nature  of  the  mechanism  by  which  an 
astronomical  telescope  is  mounted.  The  essential  point  is 
that  there  shall  be  two  axes — one  fixed,  and  pointing  at  the 
pole,  and  one  at  right  angles  to  it,  and  turning  with  it.  In 
the  arrangement  of  these  axes  there  are  great  differences  in 
the  telescopes  of  different  makers;  but  Fig.  34  shows  what 
is  essential  in  the  plan  of  mounting  now  very  generally 
adopted. 

In  the  figure  the  telescope  is  represented  as  east  of  the  spec- 
tator, and  as  pointed  at  the  pole,  and  therefore  parallel  to  the 
polar  axis.  Suppose  now  that  the  telescope  be  turned  on  the 
declination  axis,  J.5,  througli  an  arc  of  90°,  the  e^'e-piece,  jE/, 
being  brought  towards  the  spectator ;  the  object  end  will  theu 
point  towards  the  east  horizon,  and  therefore  towards  the  celes- 
tial equator,  the  eye  end  pointing  directly  towards  the  spec- 
tator. Then  let  the  whole  instrument  be  turned  on  the  polar 
axis,  the  eye-piece  being  brought  downwards.  The  telescope 
will  then  move  along  the  celestial  equator,  or  the  path  of  a 
Btar,  90°  from  the  pole.     And  at  whatever  distance  from  the 


THE  REFLECTING   TELESCOPE.  123 

pole  we  set  it  by  tuniing  it  on  the  declination  axis,  if  we 
turn  it  on  the  polar  axis  it  will  describe  a  circle  having  the 
pole  at  its  centre ;  that  is,  the  same  circle  which  a  star  follows 
by  its  dinrnal  motion.  So,  to  observe  a  star  with  the  telescope, 
we  have  first  to  turn  it  on  the  declination  axis  to  the  polar  dis- 
tance of  the  star,  and  then  on  the  polar  axis  till  it  points  at 
the  star.  This  pointing  is  effected  by  circles  divided  into  de- 
grees and  minutes,  not  sliown  in  the  figure,  by  which  the  dis- 
tance wliich  the  telescope  points  from  the  pole  and  from  the 
meridian  may  be  found  at  any  time. 

In  order  that  the  star,  when  once  found,  may  be  kept  in  the 
field  of  view,  the  telescope  is  furnished  with  a  system  of  clock- 
work, by  which  the  polar  axis  is  slowly  turned  at  the  rate  of 
one  revolution  a  day.  By  starting  this  clock-work,  the  tele- 
scope is  made  to  follow  the  star  in  its  diurnal  motion  ;  or,  to 
speak  with  greater  astronomical  precision,  as  the  earth  turns 
on  its  axis  from  west  to  east,  the  telescope  turns  from  east  to 
west  with  the  same  angular  velocity,  so  that  the  direction  in 
which  it  points  in  the  heavens  remains  unaltered. 

In  order  to  facilitate  the  finding  or  recognition  of  an  object, 
the  telescope  is  furnished  with  a  "finder,"  T,  consisting  of  a 
small  telescope  of  low  power  pointing  in  the  same  direction 
with  the  larger  one.  An  object  can  be  seen  in  the  small  tel- 
escope without  the  pointing  being  so  accurate  as  is  necessary 
in  the  case  of  the  large  one  ;  and,  when  once  seen,  the  tele^ 
scope  is  moved  until  the  object  is  in  the  middle  of  the  field 
of  view,  when  it  is  also  in  the  field  of  view  of  the  large  one. 

§  4,   The  Reflecting  Telescope. 

Two  radically  different  kinds  of  telescopes  are  made :  the 
one  just  described,  known  as  the  refracting  telescope,  because 
dependent  on  the  refraction  of  light  through  glass  lenses;  and 
the  other,  the  refiecting  telescope,  so  called  because  it  acts  by 
reflecting  the  light  from  a  concave  mirror.  The  name  of  the 
first  inventor  of  this  instrument  is  disputed ;  but  Sir  Isaac 
Newton  was  among  the  first  to  introduce  it.  It  was  designed 
by  him  to  avoid  the  difficulty  growing  out  of  the  chromatic 


124  PRACTICAL  ASTRONOMY. 

aberration  of  the  refracting  telescopes  of  his  time,  which,  it 
will  be  remembered,  were  not  achromatic.  If  parallel  ravs  of 
light  from  a  distant  object  fall  npon  a  concave  mirror,  as  shown 
in  Fig.  35,  they  will  all  be  reflected  back  to  a  focus,  F,  half- 
way between  the  centre  of  curvature,  G,  and  the  surface  of 


'^2^F^jr::::::::_^::::_:::::_:::::::z::_ ::::: 

Fig.  35. — Specnlam  bringing  rays  to  a  single  focus  by  reflection. 

the  mirror.  In  order  that  the  rajs  may  be  all  reflected  to 
absolutely  the  same  focus,  the  section  of  the  mirror  must  be 
a  parabola,  and  the  point  where  the  rays  meet  will  be  the 
focus  of  the  parabola.  If  the  rays  emanate  from  the  various 
points  of  an  object,  an  image  of  this  object  will  be  formed 
in  and  near  the  focus,  as  in  the  case  of  a  lens.  This  image 
is  to  be  viewed  with  a  maguifying  eye-piece  like  that  of  a 
refracting  telescope.     Such  a  mirror  is  called  a  speculum. 

Here,  however,  a  difliculty  arises.  The  image  is  formed  on 
the  same  side  of  the  mirror  on  which  the  object  lies;  and  in  or- 
der that  it  may  be  seen  directly,  the  eye  of  the  observer  and 
the  eye-piece  must  be  between  F  and  (7,  directly  in  the  rays 
of  light  emanating  from  the  object.  By  placing  the  eye  here, 
not  only  would  a  great  deal  of  the  light  be  cut  off  by  the  body 
of  the  observer,  but  the  definition  of  the  image  would  be  great- 
ly injured  by  the  interposition  of  so  large  an  object.  Tlu'ee 
plans  have  been  devised  for  evading  this  difticulty,  which  are 
due,  respectively,  to  Gregory,  Newton,  and  Herschel. 

The  Herschelian  Telescope.  —  In  this  form  of  telescope  the 
mirror  is  slightly  tipped,  so  that  the  image,  instead  of  being 
formed  in  the  centre  of  the  tube,  is  formed  near  one  side  of 
it,  as  in  Fig.  36.  The  observer  can  then  view  it  without  put- 
ting his  head  inside  the  tube,  and,  therefore,  without  cutting 
off  any  material  portion  of  the  light.  In  observation,  he  must 
stand  at  the  upper,  or  outer,  end  of  the  tube,  and  look  into  it, 
his  back  being  turned  towards  the  object.     From  his  looking 


THE  REFLECTING  TELESCOPE. 


125 


directly  into  the  mirror,  it  was  also  called  the  "  front-view " 
telescope.     The  great  disadvantage  of  this  arrangement  is  that 


Pig.  36. — Herschelian  telescope. 

the  rays  cannot  be  brought  to  an  exact  focus  when  they  are 
thrown  so  far  to  one  side  of  the  axis,  and  the  injury  to  the 
definition  is  so  great  that  the  front-view  plan  has  long  been 
entirely  abandoned. 

The  Newtonian  Telescope. — The  plan  proposed  by  Sir  Isaac 
Newton  was  to  place  a  small  plane  mirror  just  inside  the  fo- 
cus, inclined  to  the  telescope  at  an  angle  of  45°,  so  as  to  throw 
the  rays  to  the  side  of  the  tube,  where  they  come  to  a  focus, 
and  form  the  image.  An  opening  is  made  in  the  side  of  the 
tube,  just  below  where  the  image  is  formed  in  which  the  eye- 
piece is  inserted.  This  mirror  cuts  off  some  of  the  light,  but 
not  enough  to  be  a  serious  defect.  An  improvement  which 
lessens  this  defect  has  been  made  by  Professor  Henry  Draper. 


Fie.  37 ^Horizontal  section  of  a  Newtonian  telescope.    This  section  shows  how  the  Inmi- 

nous  rays  reflected  from  the  parabolic  mirror  M  meet  a  small  rectangular  prism  m  n, 
which  replaces  the  Inclined  plane  mirror  used  in  the  old  form  of  Newtonian  telescope. 
After  undergoing  a  total  reflection  from  in  n,  the  rays  form  at  a  b  a  very  small  image 
of  the  heavenly  body. 

The  inclined  mirror  is  replaced  by  a  small  rectangular  prism, 
by  reflection  from  which  the  image  is  formed  very  near  the 
prism.     A  pair  of  lenses  are  then  inserted  in  the  coui-se  of 


2-»1     CAST  sVi?^*" 

126  PRACTICAL  ASTEOXOMT. 

the  rays,  by  which  a  second  image  is  foiined  at  the  opening 
in  the  side  of  the  tube,  and  this  second  image  is  viewed  bv 
an  ordinary  eye -piece.  The  four  lenses  togetlier  form  an 
erecting  eye-piece. 

The  Gregorian  Telescojye. — This  is  a  form  proposed  by  James 
Gregory,  who  probably  preceded  Xewton  as  an  inventor  of  the 
reflecting  telescope.  Behind  the  focus,  F,  a  small  concave 
mirror,  B,  is  placed,  by  which  the  light  is  reflected  back  again 


Fig.  3S. — Section  of  ihe  Gregorian  telescope 

down  the  tube.  The  larger  mirror,  J/,  has  an  opening  tlirougb 
its  centre,  and  the  small  mirror,  i?,  is  so  adjusted  as  to  form  a 
second  image  of  the  object  in  this  opening.  This  image  is 
then  viewed  by  an  eye-piece  which  is  screwed  into  the  opening. 

The  Cassegrainiau  Tele-scope — In  principle  the  same  with  the 
Gregorian,  differs  from  it  only  in  that  the  small  mirror,  R,  is 
convex,  and  is  placed  inside  the  focus,  F,  so  that  the  rays  are 
reflected  from  it  before  reaching  the  focus,  and  no  image  is 
formed  until  they  reach  the  opening  in  the  large  mirror. 
This  form  has  an  advantage  over  the  Gregorian  in  that  the 
telescope  may  be  made  shorter,  and  the  small  mirror  can  be 
more  easily  shaped  to  the  required  figure.  It  has  therefore 
entirely  superseded  the  original  Gregorian  form. 

Optically,  these  forms  of  telescope  are  inferior  to  the  Xew- 
tonian.  But  tlie  latter  is  subject  to  the  inconvenience  that  the 
observer  must  be  stationed  at  the  upper  end  of  the  telescope, 
where  he  looks  into  an  eye-piece  screwed  into  the  side  of  the 
tube.  If  the  telescope  is  a  small  one,  this  inconvenience  is 
not  felt;  but  with  large  telescopes,  twenty  feet  long  or  up- 
wards, the  case  is  entirely  different.  Means  must  then  be  pro- 
vided by  which  the  observer  may  be  cari'ied  in  the  air  at  a 
height  equal  to  the  length  of  the  instrnment,  and  this  requires 
considerable  mechanism^  the  management  of  which  is  often 


THE  PRiyCIPAL   TELESCOPES  OF  MODERN  TIMES.     127 

very  troublesome.  On  the  other  hand,  the  Cassegrainian  tele- 
scope is  pointed  directly  at  the  object  to  be  viewed,  like  a  re- 
fractor, and  the  observer  stands  at  the  lower  end,  and  looks  in 
at  the  opening  through  the  large  mirror.  This  is,  therefore, 
the  most  convenient  form  of  all  in  management.  One  draw- 
back is,  that  there  are  two  mirrors  to  be  looked  after,  and,  uc 
less  the  figure  of  both  is  perfect,  the  image  will  be  distorted. 
Another  is  the  great  size  of  the  image,  which  forces  the  ob- 
server to  use  either  a  high  magnifying  power,  or  an  eye-piece 
of  corresponding  size.*  But  these  defects  are  of  little  impor- 
tance compared  with  the  great  advantage  of  convenient  use. 

§  5.  The  Principal  Great  Reflecting  Telescopes  of  Modern  Times. 

The  reflecting  telescopes  made  by  K^ewton  and  his  contem- 
poraries were  very  small  indeed,  none  being  more  than  a  few 
inches  in  diameter.  Though  vastly  more  manageable  than  the 
immensely  long  refractors  of  Huyghens,  they  do  not  seem  to 
have  exceeded  them  in  effectiveness.  We  might,  therefore, 
have  expected  the  achromatic  telescope  to  supei-sede  the  re- 
flector entirely,  if  it  could  be  made  of  large  size.  But  in  the 
time  of  Dollond  it  was  impossible  to  produce  disks  of  flint-glass 
of  sufficient  uniformity  for  a  telescope  more  than  a  very  few 
inches  in  diameter.  An  achromatic  of  four  inches  aperture 
was  then  considered  of  extraordinary  size,  and  good  ones  of 
more  than  two  or  tliree  inches  were  rare.  Consequently,  for 
the  purpose  of  seeing  the  most  faint  and  difficult  objects,  the 
earlier  achromatics  were  little,  if  any,  better  than  the  long 
telescopes  of  Huj'ghens  and  Cassini.  As  there  were  no  such 
obstacles  to  the  polishing  of  large  mirrors,  it  was  clear  that  it 
was  to  the  reflecting  telescope  that  recourse  must  be  had  for 
any  great  increase  in  optical  power.  Before  tlie  middle  of 
the  last  century  the  reflectors  were  little  larger  than  the  re- 
fractors, and  had  not  exceeded  them  in  their  optical  perform 
ance.  But  a  genius  now  arose  who  was  to  make  a  wonderful 
improvement  in  their  construction. 

*  The  Melbourne  telescope  has  an  eve-lens  si.\  inches  in  diameter. 

G  lo' 


12S  PBACTICAL  ASTBOXOifV. 

William  Hei-scliel,  in  1766,  was  a  church-organist  and  teach- 
er of  music  of  very  high  i-epute  in  Bath,  who  spent  what  little 
leisure  he  had  in  the  study  of  mathematics,  astronomy,  and 
optics.  By  accident  a  Gregorian  reflector  two  feet  long  feli 
into  his  hands,  and,  turning  it  to  the  heavens,  he  was  so  enrapt- 
ured with  the  views  presented  to  him  that  he  sent  to  London 
to  see  if  he  could  not  purchase  one  of  greater  power.  The 
price  named  being  far  above  his  means,  he  resolved  to  make 
one  for  himself.  After  many  experiments  with  metallic  al- 
loys, to  learn  which  would  reflect  most  light,  and  many  efforts 
to  And  the  best  way  of  polishing  his  mirror,  and  giving  it  a 
parabolic  form,  he  produced  a  flve-foot  XeM'tonian  reflector, 
which  revealed  to  him  a  number  of  interesting  celestial  phe- 
nomena, though,  of  course,  nothing  that  was  not  already  known. 
Determined  to  aim  at  nothing  less  than  the  largest  telescope 
that  could  be  made,  he  attempted  vast  numbei'S  of  mirrors  of 
constantly  increasing  size.  The  large  majority  of  the  individ- 
ual attempts  were  failures ;  but  among  the  results  of  the  suc- 
cessful attempts  were  telescopes  of  constantly  increasing  size, 
until  he  attained  the  hitherto  untliought-of  aperture  of  two  feet, 
with  a  lenjrth  of  twentv  feet.  With  one  of  these  he  discov- 
ered  the  planet  Uranus.  The  fame  of  the  musician-astrono- 
mer reaching  the  ears  of  King  George  III.,  that  monarch  gave 
him  a  pension  of  £200  per  annum,  to  enable  him  to  devote 
his  life  to  a  career  of  astronomical  discovery.  He  now  made 
the  greatest  stride  of  all  by  completing  a  reflector  four  feet 
in  diameter  and  forty  feet  long,  with  which  he  discovered  two 
new  satellites  of  Saturn. 

Hei-schel  now  found  tliat  he  had  attained  the  limit  of  man- 
ageable size.  The  observer  had  to  be  suspended  perhaps  thir- 
ty or  forty  feet  in  the  air,  in  a  room  large  enough  to  hold,  not 
only  himself,  but  all  the  means  necessary  for  recording  his 
observations ;  and  this  room  had  to  follow  the  telescope  as  it 
moved,  to  keep  a  star  in  the  field.  To  this  was  added  the 
diificulty  of  keeping  the  mirror  in  proper  figure,  the  mere 
change  of  temperature  in  the  night  operating  injuriousl}*  in 
this  respect.     We  need  not,  therefore,  be  surprised  to  learn 


THE  PEINCIPAL  TELESCOPES  OF  MODERN  TIMES.     129 


Fig.  39. — Herschel's  great  telescope. 

that  Ilerschel  made  very  little  use  of  this  instrument,  and  pre- 
ferred the  twenty-foot  even  in  scrutinizing  the  most  difficult 
objects.* 

*  Herschel's  great  instrument  is  still  preserved,  but  is  not  mounted  for  use; 
indeed,  it  is  probable  tliat  the  mirror  lost  all  its  lustre  long  years  ago.  In  1 839, 
Sir  John  Herschel  dismounted  it,  hiid  it  in  a  iiorizontal  position,  and  closed  it  up 
after  a  family  celebration  inside  the  tube,  at  wiiich  the  following  song  was  sung : 

THE  OLD  TELESCOPE. 

[To  he  sung  on  New-year' 8-eve,  lS39-'-10,  by  Papa,  Mamma,  Madame  Gerlach,  and  all  the  LittI 
Bodies  in  the  Tube  thereof  assembled.^ 

In  the  old  Telescope's  tube  we  sit, 
And  the  shades  of  the  past  around  us  flit; 
His  requiem  siuj;  we  with  shout  and  diu, 
While  the  old  year  goes  out,  and  the  new  comes  In. 
Charus. — Merrily,  merrily  let  us  all  sing, 

Aud  make  the  old  telescope  rattle  and  ring ! 


130  PRACTICAL  ASTRONOMY. 

The  only  immediate  successor  of  Sir  "William  Herschel  in 
the  construction  of  great  telescopes  was  his  son,  Sir  John  Her- 
schel. But  the  latter  made  none  to  equal  the  largest  of  his 
fathers  in  size,  and  it  is  doubtful  whether  thej  exceeded  them 
in  optical  power. 

The  first  decided  advance  on  the  great  telescope  was  the 
celebrated  reflector  of  the  Earl  of  Eosse,*  at  Parsoustown,  Ire- 


Fnll  fifty  years  did  he  laugh  at  the  storm, 
And  the  blast  could  not  shake  his  majestic  form ; 
Now  prone  he  lies,  where  he  once  stood  high, 
And  searched  the  deep  heaven  with  his  broad,  bright  eye. 
CAorus.— Merrily,  merrily,  etc.,  etc. 

There  are  wonders  no  living  sight  has  seen. 
Which  within  this  hollow  have  pictured  been ; 
Which  mortal  record  can  never  recall. 
And  are  known  to  Him  only  who  made  them  alL 
Chorus. — ^Merrily,  merrily,  etc.,  etc. 

Here  watched  our  father  the  wintry  night. 
And  his  gaze  has  been  fed  with  preadamite  light. 
His  labors  were  lightened  by  sisterly  love, 
And,  united,  they  strained  their  vision  above. 
C/iorus.— Merrily,  merrily,  etc,  etc 

He  has  stretched  liim  quietly  down,  at  length. 
To  bask  in  the  starlight  his  giant  strength ; 
And  Time  shall  here  a  tough  morsel  find 
For  his  steel-devouring  teeth  to  grind. 
Chorus. — Merrily,  merrily,  etc,  etc 

He  will  grind  it  at  last,  as  grind  it  he  must. 
And  its  brass  and  its  iron  shall  be  clay  and  rust ; 
But  scathless  ages  shall  roll  away, 
And  nurture  its  frame,  and  its  form's  decaj. 
CRortM.— Merrily,  merrily,  etc.,  etc 

A  new  year  dawns,  and  the  old  year's  past ; 
God  send  it,  a  happy  one  like  the  last 
(A  little  more  sun  and  a  little  less  rain 
To  save  ns  from  cough  and  rheumatic  pain). 
Cftoru*.— Merrily,  merrily,  etc.,  etc. 

Ciod  grant  that  its  end  this  group  may  find 
In  love  and  in  harmony  fondly  joined ! 
And  that  some  of  us.  fifty  years  hence,  once  more 
May  make  the  old  Telescope's  echoes  roar. 
Chorus. — Merrily,  merrily,  etc.,  etc 

*  William  Parsons,  third  Earl  cf  Rosse,  the  original  constrnctor  of  this  tele- 
scope, died  in  1867.  The  work  of  the  instrument  is  continued  by  his  son,  the  pres- 
ent earL 


THE  PRINCIPAL  TELESCOPES  OF  MODERN  TIMES.     133 

land.  The  speculum  of  this  telescope  is  six  feet  in  diameter, 
and  about  fifty-four  feet  focal  length,  and  was  cast  in  1842. 
One  of  the  great  improvements  made  by  the  Earl  of  Rosse 
was  the  introduction  of  steam  machinery  for  grinding  and 
polishing  the  great  mirror,  an  instrumentality  of  which  Her- 
schel  could  not  avail  himself.  TJie  mounting  of  this  telescope 
is  decidedly  different  from  that  adopted  by  Herschel.  The 
telescope  is  placed  between  two  walls  of  masonry,  which  only 
allow  it  to  move  about  10°  on  each  side  of  the  meridian,  and 
it  turns  on  a  pivot  at  the  lower  end  of  the  tube.  It  is  moved 
north  and  south  in  the  meridian  by  an  ingenious  combination 
of  chains,  and  may  thus  be  set  at  the  polar  distance  of  any 
star  which  it  is  required  to  observe.  It  is  then  moved  slowly 
towards  the  west,  so  as  to  follow  the  star,  by  a  long  screw 
driven  by  an  immense  piece  of  clock-work.  It  is  commonly 
used  as  a  Newtonian,  the  observer  looking  into  the  side  of  the 
tube  near  the  upper  end.  To  enable  him  to  reach  the  mouth 
of  the  tube,  various  systems  of  movable  platforms  and  staging 
are  employed.  One  of  the  platforms  is  suspended  south  of 
the  piers  ;  it  extends  east  and  west  by  the  distance  between 
the  walls,  and  may  be  raised  by  machinery  so  as  to  be  directly 
under  the  mouth  of  the  telescope  so  long  as  the  altitude  of  the 
latter  is  less  than  45°.  When  the  altitude  is  greater  than  this, 
the  observer  ascends  a  stairway  to  the  top  of  one  of  the  walls, 
where  he  mounts  one  of  several  sliding  stages,  by  which  he 
can  be  carried  to  the  mouth  of  the  telescope,  in  any  position 
of  the  latter.  This  instrument  has  been  employed  principal- 
ly in  making  drawings  of  lunar  scenery  and  of  the  planets 
and  nebulae.  Its  great  light-gathering  power  peculiarly  fits  it 
for  the  latter  object. 

Other  Reflecting  Telescopes. — Although  no  other  reflector  ap- 
proaching the  great  one  of  the  Earl  of  Rosse  in  size  has  ever 
been  made,  some  others  are  worthy  of  notice,  on  account  of 
their  perfection  of  figure  and  the  importance  of  the  discov- 
eries made  with  them.  Among  these  the  first  place  is  due  to 
the  great  reflectors  of  Mr.  William  Lassell,  of  England.  This 
gentleman  mada-  a  reflector  of  two  feet  aperture  about  the 


134 


PRACTICAL  ASTRONOMY. 


same  time  that  Rosse  constructed  his  immense  six-foot.  The 
perfection  of  figure  of  the  mirror  was  evinced  by  the  discov- 
ery of  two  satellites  of  Uranus,  which  had  been  previously  un- 
known and  unseen,  unless,  as  is  possible,  Herschel  and  Struve 
caught  glimpses  of  them  on  a  few  occasions.  He  afterwards 
made  one  of  four  feet  aperture,  which,  in  1863,  he  took  to  the 
island  of  Malta,  where  he  made  a  series  of  observations  on 
satellites  and  nebulae. 


Fig.  41. — Mr.  Lassell's  great  four-foot  reflector,  as  mounted  at  Malta. 

In  1870,  a  reflecting  telescope  four  feet  in  diameter,  on  the 
Cassegrainian  plan,  was  made  by  Thomas  Grubb  &  Son,  of 
Dublin,  for  the  Observatory  of  Melbourne,  Australia.  This 
instrument  is  remarkable,  not  only  for  its  perfection  of  figure, 
but  as  being  probably  the  most  easily  managed  large  reflector 
ever  made. 


Fig.  42.— The  uew  Paris  reflector. 


THE  PRINCIPAL   TELESCOPES   OF  MODERN  TIMES.     137 

The  only  American  who  ever  successfully  undertook  the 
construction  of  large  reflecting  telescopes  was  the  late  Pro- 
fessor Henry  Draper,  of  New  York,  who  had  one  of  twenty- 
eiglit  inches  aperture,  the  work  of  his  own  hands.  This  in- 
strument was  mounted  about  1S72  in  the  owner's  private  ob- 
servatory at  Hastings,  on  the  Hudson.  The  mirror  is  not  of 
speculum  metal,  but  of  silvered  glass,  and  is  almost  perfect  in 
figure.  This  telescope  has  been  principally  employed  in  mak- 
ing photographs  of  celestial  objects,  and  can  be  used  either  as 
a  Newtonian  or  a  Cassegrainian. 

In  1876  a  silvered  glass  reflecting  telescope,  four  feet  in  di- 
ameter, made  by  Mr.  A.  Martin,  was  mounted  at  the  Paris 
observatory.  The  machinery  for  supporting  and  moving  this 
telescope  being  in  some  respects  peculiar,  we  present  a  view 
of  it  in  Fig.  42,  on  the  preceding  page.  It  has  never  been 
successful  in  forming  good  images  of  the  stars ;  but  it  is  not 
known  whether  the  defects  are  in  the  figure  of  the  mirror,  or 
arise  from  defective  methods  of  supporting  it. 

Mr.  A.  A.  Common,  of  Ealing,  England,  is  the  possessor  of 
one  of  the  most  successful  reflecting  telescopes  of  the  present 
day.  It  is  the  joint  work  of  himself  and  Mr.  Calver,  and  is 
thirty-seven  inches  in  diameter.  Like  other  recent  reflectors, 
it  is  of  silvered  glass.  It  has  been  principally  employed  in 
photographing  nebulae  and  other  celestial  objects,  a  work  in 
which  its  owner  has  been  remarkably  successful. 

§  6.   Great  Refracting  Telescopes. 

We  have  already  remarked  that,  in  the  early  days  of  the 
achromatic  telescope,  its  progress  was  hindered  by  the  difti- 
culty  of  making  large  disks  of  flint-glass.  About  the  begin- 
ning of  the  present  century,  Guinand,  a  Swiss  mechanic,  after 
a  long  series  of  experiments,  discovered  a  method  by  which 
he  could  produce  disks  of  flint-glass  of  a  size  before  unheard 
of.  The  celebrated  Fraunhofer  was  then  commencing  busi- 
ness as  an  optician  in  Munich,  and  hearing  of  Guinand's  suc- 
cess induced  him  to  come  to  Munich  and  commence  the  man- 
ufacture of  optical  glass.     Fraunhofer  was  a  physicist  of  a 


138 


PBACIICAL  ASTRONOMY. 


Pig.  43.— The  great  Melbourne  reflector.  T,  the  tube  containing  the  great  mirror  near  Its 
lower  end.  T,  the  small  mirror  throwing  the  light  back  to  the  eye-piece,  y.  C  N,  the 
polar  axis,  U.  the  counterpoise  at  the  end  of  the  declination  axis.  Z,  the  clock-work 
which  moves  the  telescojje  by  the  jointed  rods  z  e  e  E,  and  the  clamp  F. 

high  order,  and  made  a  more  careful  and  exhaustive  study  of 
the  optical  qualities  of  glass,  and  the  conditions  for  making 
the  best  telescope,  than  any  one  before  him  had  ever  attempted. 
With  the  aid  of  the  large  disks  furnished  b}'  Guinand,  he  was 
able  to  carry  the  aperture  of  his  telescopes  up  to  ten  inches. 
Dying  in  1826,  his  successoi*s,  Merz  and  Mahler,  of  Munich, 
made  two  telescopes  of  fifteen  inches  aperture,  which  were 
then  considered  most  extraordinary.     One  of  these  belongs 


GREAT  REFRACTING  TELESCOPES.  139 

to  the  Pulkowa  Observatory,  in  Russia ;  and  the  other  was 
purchased  by  a  subscription  of  citizens  of  Boston  for  tlie  ob- 
servatory of  Harvard  University. 

No  rival  of  the  house  of  Fraunhofer  in  the  construction  of 
great  refractors  arose  until  he  had  been  dead  thirty  years,  and 
then  it  arose  where  least  expected.  In  1846,  Mr.  Alvan  Clark 
was  a  citizen  of  Cambridgeport,  Massachusetts,  unknown  to 
fame,  wlio  made  a  modest  livelihood  by  pursuing  the  self- 
taught  art  of  portrait -painting,  and  beguiled  his  leisure  by 
the  construction  of  small  telescopes.  Though  without  the 
advantage  of  a  mathematical  education,  he  had  a  perfect 
knowledge  of  optical  principles  to  just  the  extent  necessary 
to  enable  him  to  make  and  judge  a  telescope.  Having  been 
led  by  accident  to  attempt  the  grinding  of  lenses,  he  soon  pro- 
duced objectives  equal  in  quality  to  any  ever  made,  and,  if 
he  had  been  a  citizen  of  any  other  civilized  country,  would 
have  found  no  difficulty  in  establishing  a  reputation.  But 
he  had  to  struggle  ten  years  with  tliat  neglect  and  incre- 
dulity which  is  the  common  lot  of  native  genius  in  this  coun- 
try ;  and,  extraordinary  as  it  may  seem,  it  was  by  a  foreigner 
that  his  name  and  powers  were  first  brought  to  the  notice 
of  the  astronomical  world.  Rev.  "W.  R.  Dawes,  one  of  the 
leading  amateur  astronomers  of  England,  and  an  active  mem- 
ber of  the  Royal  Astronomical  Society,  purchased  an  object- 
glass  from  Mr.  Clark  in  1853.  He  found  it  so  excellent  that 
in  the  course  of  the  next  two  or  three  years  he  ordered  several 
others,  and,  finally,  an  entire  telescope.  He  also  made  several 
communications  to  the  Astronomical  Society,  giving  lists  of 
difficult  double  stars  detected  by  Mr.  Clai-k  with  telescopes  of 
his  own  construction,  and  showing  that  Mr.  Clark's  objectives 
were  almost  perfect  in  definition. 

The  result  of  this  was  that  the  American  artist  began  to  be 
appreciated  in  his  own  country ;  and  in  1860  he  received  an 
order  from  the  University  of  Mississippi,  of  which  Dr.  F.  A. 
P.  Barnard*  was  then  president,  for  a  refractor  of  eighteen 

*  Now  President  of  Columbia  College,  New  York  City. 


14:0  PRACTICAL  ASTRONOMY. 

inches  aperture,  which  was  three  inches  greater  than  the  larg. 
est  that  had  then  been  made.  Before  the  glass  was  finished, 
it  was  made  famous  by  tlie  discover}'  of  tlie  companion  of 
Sirins,  a  success  for  whicli  the  Lalande  medal  was  awarded 
by  the  French  Academy  of  Sciences.  The  University  of 
Mississippi  was  prevented  from  taking  this  telescope  by  the 
civil  war.  It  was  sold  to  the  Astronomical  Society  of  Chi- 
cago, and  is  now  mounted  at  the  University  in  that  city. 

The  construction  of  this  telescope  was  the  first  of  a  series  of 
works  by  Mr,  Clark  and  his  two  sons  which  have  revolution- 
ized the  optical  branch  of  astronomy;  yet  the  firm  had  to  wait 
eight  years  after  the  completion  of  the  Chicago  telescope  be- 
fore a  larger  one  was  ordered.  Two  great  ones  were  then 
made  at  the  same  time. 

Up  to  1870  the  Naval  Observator}'  of  the  United  States  had 
no  large  telescope  except  a  Munich  refractor  of  nine  and  a  half 
inches,  such  as  Fraunliofer  used  to  make  early  in  the  century. 
In  that  year  Congress  authorized  the  construction  of  a  telescope 
of  the  largest  size,  of  American  manufacture.  A  conti'act  was 
soon  after  made  with  the  firm  of  Alvan  Clark  &  Sons  to  con- 
struct the  telescope.  The  aperture  agreed  upon  was  twenty- 
six  inches.  The  rough  disks  were  ordered  from  Messrs.  Chance 
&  Co.,  of  Birmingham,  England ;  but  so  great  was  the  diffi- 
culty of  making  large  masses  of  glass  of  the  necessary  purity 
that  they  did  not  arrive  until  December,  1871.  Tlie  work  of 
figuring  and  polishing  them  was  commenced  immediately. 
The  glasses  were  completed  in  October,  1872,  and  the  remain- 
der of  the  instrument  during  the  year  following.  It  was  final- 
ly mounted  and  ready  for  observation  in  November,  1873. 
This  telescope  has  since  become  famous  through  the  discovery 
of  the  satellites  of  Mars. 

When  this  telescope  Avas  ordered  from  the  Messrs.  Clark 
they  were  negotiating  with  Mr.  L.  B.  McCormick,  of  Chicago, 
for  a  telescope  of  equal  size.  This  instrument  has  since  been 
completed,  and  presented  by  its  owner  to  the  University  of 
Virginia,  where  it  is  doing  good  work  in  the  hands  of  Pro- 
fessor Ormoud  Stone. 


GREAT  REFRACTING   TELESCOPES.  141 

For  some  ten  years  the  Washington  telescope  was  the  great- 
est  refractor  of  the  world  in  actual  use.  The  order  for  an 
instrument  which  should  exceed  it  in  aperture  came  from 
Russia.  Tlie  great  observatory  of  Pnlkowa,  completed  about 
1840,  is  among  the  most  successful  of  the  world.  Its  telescope 
of  fifteen  inches  aperture,  the  twin  brother  of  the  Harvard 
College  telescope,  though  a  marvel  when  it  was  constructed, 
was  far  outdone  by  the  telescopes  of  recent  times.  In  1S7S 
the  Government  authorized  a  much  larger  one;  and  the  year 
following,  after  a  visit  by  Director  Struve  to  the  principal  opti- 
cal establishments  of  Europe  and  America,  it  was  decided  to 
order  an  objective  of  thirty  inches  aperture  from  the  Messrs. 
Clark.  The  latter  ordered  the  rough  disks  from  Fell,  of  Paris. 
More  than  two  years  were  required  for  their  successful  found- 
ing, so  tliat  the  objective  was  not  finally  completed  until  1883. 
In  1884  the  mounting  was.  erected  by  the  celebrated  firm  of 
Repsolds,  in  Hamburg,  and  the  telescope  was  in  successful  use 
in  the  summer  of  1885. 

The  Great  Lick  Tdescojje.  —  In  1874  Mr.  James  Lick,  a 
wealthy  resident  of  San  Francisco,,  made  arrangements  for 
founding  an  observatory,  to  contain  the  largest  and  most  pow- 
erful telescope  ever  made.  The  legal  complications  which 
followed  his  death  in  1876  required  four  years  for  their  set- 
tlement, and  it  was  not  until  1880  that  a  contract  was  made 
with  Alvan  Clark  &  Sons  for  an  objective  of  thirty-six  inches 
aperture.  Feil,  of  Paris,  was  the  only  person  who  could  hope- 
fully undertake  the  casting  of  disks  of  such  size,  and  he  found 
the  task  so  difficult  that  it  was  not  until  1885  that  both  disks 
were  completed.  Their  quality  was  so  fine  that  the  Clarks 
had  the  objective  ready  for  delivery  in  November,  1886. 
The  mounting  of  the  telescope  was  made  by  Warner  &  Swa- 
ze}'',  of  Cleveland,  and  the  great  telescope  was  put  into  place 
on  Mount  Hamilton  in  the  summer  of  1888. 

The  American  artists  have  not  been  without  worthy  rivals 
abroad.  In  1869  Thomas  Cooke  &  Sons,  of  England,  made 
a  25-inch  telescope  for  Mr.  R.  S.  Newall,  which  was  for  a 
few  years  the  largest  refractor  in  existence.     In  1882  Mr. 


142  PRACTICAL  ASTRONOMY. 

Howard  Grubb,  of  Dublin,  completed  a  27-incli  telescope  for 
the  Vienna  observatory.  Final!}-,  in  18S6,  the  brothers  Henry, 
of  Paris,  completed  a  30-incli  glass  for  the  observatory  of  Nice, 
France. 

The  Lick  telescope  is  not,  however,  likely  to  be  soon  sur- 
passed. The  great  cost  of  a  larger  instrument,  the  difficulty 
of  casting  large  disks,  and  the  recent  death  of  Feil,  the  only 
glass-maker  who  has  yet  succeeded  in  making  a  good  36-inch 
disk,  must  all  combine  to  discourage  any  speedy  attempts  in 
this  dhection. 

§  7.  The  Magnifying  Powers  of  the  Two  Classes  of  Telescopes. 

Questions  which  now  very  naturally  arise  are,  Which  of  the 
two  classes  of  telescopes  we  have  described  is  the  more  power- 
ful, the  reflector  or  the  refractor  ?  and  is  there  any  limit  to  the 
magnifying  power  of  either  ?  To  these  questions  it  is  difficult 
to  return  a  decided  answer,  because  each  class  has  its  peculiar 
advantages,  and  in  each  class  many  difficulties  lie  in  the  way 
of  obtaining  the  highest  magnifying  power.  The  fact  is,  that 
very  exaggerated  ideas  of  the  magnifying  power  of  great  tele- 
scopes are  entertained  by  the  public.  It  will,  therefore,  be 
instructive  to  state  what  the  circumstances  are  which  prevent 
these  ideas  from  being  realized,  and  what  the  conditions  are 
on  which  the  seeing  power  of  telescopes  depends. 

We  note,  fii-st,  that  when  we  look  at  a  luminous  point — a  star, 
for  instance — without  a  telescope,  we  see  it  by  the  aid  of  the 
cone  of  light  which  enters  the  pupil  of  the  eye.  The  diameter 
of  the  pupil  being  about  one-fifth  of  an  inch,  as  much  light 
from  the  star  as  falls  on  a  circle  of  this  diameter  is  broug^ht  to 
a  focus  on  the  retina,  and  unless  this  quantity  of  light  is  suffi- 
cient to  be  perceptible,  the  star  will  not  be  seen.  ISTow,  we 
may  liken  the  telescope  to  a  "  Cyclopean  eye,"  of  which  the 
object-glass  is  the  pupil,  because,  by  its  aid,  all  the  light  which 
falls  on  the  object-glass  is  brought  to  a  focus  on  the  retina, 
provided  that  a  sufficiently  small  eye-piece  is  used.  Of  course, 
we  must  except  that  portion  of  the  light  which  is  lost  in  pass- 
ing through  the  glasses.     Since  the  quantity  of  light  which 


MAGNIFYING  POWERS  OF  TELESCOPES.  143 

falls  oil  a  surface  is  proportional  to  the  extent  of  the  surface, 
and  therefore  to  the  square  of  its  diameter,  it  follows  that, 
because  a  telescope  of  one-inch  clear  aperture  has  live  times 
the  diameter  of  the  pupil,  it  will  admit  25  times  the  light;  a 
six-inch  will  admit  900  times  the  light  which  the  pupil  will ; 
and  so  with  any  other  aperture.  A  star  viewed  with  the 
telescope  will,  therefore,  appear  brighter  than  to  the  naked 
eye  in  proportion  to  the  square  of  the  aperture  of  the  in- 
strument. But  the  star  will  not  be  magnified  like  a  planet, 
because  a  point  is  only  a  point,  no  matter  how  often  we  mul- 
tiply it.  It  is  true  that  a  bright  star  in  the  telescope  some- 
times appears  to  have  a  perceptible  disk;  but  this  is  owing  to 
various  imperfections  of  the  image,  having  their  origin  in  the 
air,  the  instrument,  and  the  eye,  all  of  which  have  the  effect  of 
slightly  scattering  a  portion  of  the  light  which  comes  from  the 
star.  Hence,  with  perfect  vision  the  apparent  brilliancy  of  a 
star  will  be  proportional  to  the  square  of  the  aperture  of  the 
telescope.  It  is  said  that  Sir  William  Ilerschel,  at  a  time  when 
by  accident  his  telescope  M'as  so  pointed  that  Sirius  Avas  about 
to  enter  its  field  of  view,  was  first  apprised  of  what  was  com- 
ing by  the  appearance  of  a  dawn  like  the  morning.  The  light 
increased  rapidly,  until  the  star  itself  appeared  with  a  dazzling 
splendor  which  reminded  him  of  the  rising  sun.  Indeed,  in 
any  good  telescope  of  two  feet  aperture  or  upwards,  Sirius  is 
an  almost  dazzling  object  to  an  eye  which  has  rested  for  some 
time  in  darkness. 

But  in  order  that  all  the  light  which  falls  on  the  object- 
glass,  or  mirror,  of  a  telescope  may  enter  the  pupil  of  the  eye, 
it  is  necessary  that  the  magnifying  power  be  at  least  equal  to 
the  ratio  which  the  aperture  of  the  telescope  bears  to  tliat  of 
the  pupil.  The  latter  is  generally  about  one-fifth  of  an  inch. 
We  must,  therefore,  enq^loy  a  magnifying  power  of  at  least 
live  for  every  inch  of  aperture,  or  we  will  not  get  the  full  ad- 
vantage of  our  object-glass.  The  reason  of  this  will  be  appar- 
ent by  studying  Fig.  29,  p.  Ill,  from  which  it  will  be  seen  that 
a  pencil  of  parallel  rays  falling  on  the  object-glass,  and  pass- 
ing through  the  eye-piece,  will  be  reduced  in  diameter  in  the 

11 


144  PEACTICAL   ASTRONOMY. 

ratio  of  the  focal  distance  of  the  objective  to  that  of  the  eye- 
piece, which  is  the  same  as  the  magnifying  power.  For  in- 
stance, if  to  a  2:}:-inch  telescope  we  attached  an  eye-piece  so 
large  that  tlie  magnifying  power  was  only  48,  and  pointed  it 
at  a  star,  the  "emergent  pencil"  of  rays  from  the  eye-piece 
would  be  half  an  inch  in  diameter,  and  the  whole  of  them 
could  not  enter  the  pupil.  In  order  that  all  the  light  falling 
on  a  24-inch  glass  may  enter  the  eye,  the  magnifying  power 
must  be  at  least  120. 

Still  another  cause  which  places  a  limit  to  the  power  of 
telescopes  is  diffraction.  When  the  "  emergent  pencil "  is 
reduced  below  -gL  of  an  inch  in  diameter — that  is,  when  the 
magnifying  power  is  greater  than  50  for  every  inch  of  aper- 
ture of  the  object-glass — the  outlines  of  eveiy  object  observed 
become  confused  and  indistinct,  no  matter  how  bright  the  il- 
lumination or  how  perfect  the  glass  may  be.  The  effect  is  the 
same  as  if  we  looked  through  a  small  pin-hole  in  a  card,  an 
experiment  which  anyone  may  try.  This  effect  is  owing  to 
the  diffraction  of  the  light  at  the  edge  of  the  object-glass  or 
mirror,  and  it  increases  so  rapidly  with  the  magnifying  power 
that  when  we  carry  the  latter  above  100  to  the  inch,  the  in- 
crease of  indistinctness  neutralizes  the  increase  of  power.  If, 
then,  we  multiply  the  aperture  of  the  telescope  in  inches  by 
100,  we  shall  have  a  limit  beyond  which  there  is  no  use  in 
magnifying.  Indeed,  it  is  doubtful  if  any  real  advantage  is 
gained  beyond  60  to  the  inch.  In  a  telescope  of  two  feet  (24 
inches)  aperture  this  limit  would  be  2400.  Such  a  limit  can- 
not be  set  with  entire  exactness;  but,  even  under  the  most  fa- 
vorable circumstances,  the  advantage  in  attempting  to  surpass 
a  power  of  70  to  the  inch  will  be  very  slight. 

The  foregoing  remarks  apply  to  the  most  perfect  telescopes, 
used  under  the  most  favorable  circumstances.  But  the  best 
telescope  has  imperfections  which  would  nearly  always  pre- 
vent the  use  of  the  highest  magnifying  powers  in  astronomical 
observations.  In  the  refracting  telescope  the  principal  defect 
arises  from  the  secondary  aberration  already  explained,  which, 
arising  from  an  inherent  quality  of  the  glass  itself,  cannot  be 
obviated  by  perfection  of  workmanship     In  the  case  of  the  re 


MAGNIFYING  POWERS  OF  TELESCOPES.  145 

flector,  the  corresponding  difficulty  is  to  keep  the  mirror  in  per- 
fect figure  in  every  position.  As  the  telescope  is  moved  about, 
the  mirror  is  liable  to  bend,  through  its  own  weight  and  elas- 
ticity, to  such  an  extent  as  greatly  to  injure  or  destroy  the  im- 
age in  the  focus ;  and,  though  this  liability  is  greatly  dimin- 
ished by  the  plan  now  adopted,  of  supporting  the  mirror  on  a 
system  of  levers  or  on  an  air-cushion,  it  is  generally  trouble- 
some, owing  to  the  difficulty  of  keeping  the  apparatus  in  order. 
If  we  compare  the  refracting  and  reflecting  telescopes  which 
have  hitherto  been  made,  it  is  easy  to  make  a  summary  of 
their  relative  advantages.  If  properly  made  and  attended  to, 
the  refractor  is  easy  to  manage,  convenient  in  use,  and  al- 
ways in  order  for  working  with  its  full  power.  If  its  greatest 
defect,  the  secondary  spectrum,  cannot  be  diminished  by  skill, 
neither  can  it  be  increased  by  tlie  want  of  skill  on  the  part  of 
the  observer.  So  important  is  this  certainty  of  operation,  that 
far  the  greater  part  of  the  astronomical  observations  of  the 
present  century  have  been  made  with  refractors,  which  have 
always  proved  themselves  the  best  working  instruments.  Still, 
the  defects  arising  from  the  secondary  spectrum  are  inherent 
in  the  latter,  and  increase  with  the  aperture  of  the  glass  to 
such  an  extent  that  no  advantage  can  ever  be  gained  by  carry- 
ing the  diameter  of  the  lenses  beyond  a  limit  which  may  be 
somewhere  between  30  and  36  inches.  On  the  other  hand, 
when  we  consider  mere  seciiig-power,  calculation  at  least  gives 
the  preference  to  the  reflector.  It  is  easy  to  compute  that 
Lord  Ttosse's  "Leviathan,"  and  the  four-foot  reflectors  of  Mr. 
Lassell  and  of  the  Paris  and  Melbourne  observatories,  must 
collect  from  two  to  four  times  the  light  of  the  great  Washing- 
ton telescope.  But  when,  instead  of  calculation,  M-e  inquire 
what  difficult  objects  have  actually  been  seen  with  the  two 
classes  of  instruments,  the  result  seems  to  indicate  that  the 
greatest  refractor  is  equal  in  optical  power  to  the  great  reflect- 
ors. No  known  object  seen  with  the  latter  is  too  faint  to  be 
seen  with  the  former.  Why  this  discrepancy  between  the 
calculated  powers  of  the  great  reflectors  and  their  actual  per- 
formance I     The  only  causes  we  can  find  for  it  are  imperfec- 


146  PRACTICAL  ASTRONOMY. 

tions  in  the  figure  and  polish  of  the  great  mirrors.  The  great- 
refractors  are  substantially  perfect  in  their  workmanship ;  the 
reflectors  do  not  appear  to  be  perfect,  though  wliat  the  imper- 
fections may  be,  it  is  impossible  to  say  with  entire  certainty. 
Whether  the  great  telescope  of  the  future  shall  belong  to  the 
one  class  or  the  other  must  depend  upon  whether  the  imper- 
fections of  the  reflecting  mirror  can  be  completely  overcome. 
Mr.  Grubb,  the  maker  of  the  great  Melbourne  telescope,  thinks 
he  has  completely  succeeded  in  this,  so  as  to  insure  a  mirror 
of  six,  seven,  or  even  eight  feet  in  diameter  which  shall  be  as 
perfect  as  an  object-glass.  If  he  is  right  —  and  there  is  no 
mechanician  wliose  opinion  is  entitled  to  greater  confidence — 
then  he  has  solved  the  problem  in  favor  of  the  reflector,  so  far 
as  optical  power  is  concerned.  But  so  large  a  telescope  will 
be  so  diflScult  to  manipulate,  that  we  must  still  look  to  the  re- 
fractor as  the  working  instrument  of  the  future  as  well  as  of 
the  past;  though,  for  the  discovery  and  examination  of  vei-y 
faint  objects,  it  may  be  found  that  the  advantage  will  all  be 
on  the  side  of  the  future  great  reflector. 

The  great  foe  to  astronomical  observation  is  one  which 
people  seldom  take  into  account,  namely,  the  atmosphere. 
When  we  look  at  a  distant  object  along  the  surface  of  the 
ground  on  a  hot  summer  day,  we  notice  a  certain  waviness  of 
outline,  accompanied  by  a  slight  trembling.  If  we  look  with 
a  telescope,  we  shall  find  this  waving  and  trembling  magnified 
as  much  as  the  object  is,  so  that  we  can  see  little  better  with 
the  most  powerful  telescope  than  with  the  naked  eye.  The 
cause  of  this  appearance  is  the  mixing  of  the  hot  air  near  the 
ground  with  the  cooler  air  above,  which  causes  an  irregular 
and  constantly  changing  refraction,  and  the  result  is  that  as- 
tronomical observations  requiring  high  magnifying  power  can 
very  rarely  be  advantageously  made  in  the  daytime.  By 
night  the  air  is  not  so  much  disturbed,  yet  there  are  always 
currents  of  air  of  slightly  different  temperatures,  the  crossing 
and  mixing  of  which  produce  the  same  effects  in  a  small  da 
gree.  To  such  currents  is  due  the  twinkling  of  the  stars; 
and  we  may  lay  it  down  as  a  rule,  that  when  a  star  twinkles 


MAGNIFYING  POWERS  OF  TELESCOPES.  147 

the  finest  observation  of  it  cannot  be  made  with  a  telescope  of 
high  power.  Instead  of  presenting  the  appearance  of  a  bright, 
well-defined  point,  it  will  look  like  a  blaze  of  light  flaring 
about  in  every  direction,  or  like  a  pot  of  molten  boiling  metal ; 
and  the  higher  the  magnifying  power,  the  more  it  will  flare 
and  boil.  The  amount  of  this  atmospheric  disturbance  varies 
greatly  from  night  to  night,  but  it  is  never  entirely  absent. 
If  no  continuous  disturbance  of  the  image  could  be  seen  with 
a  power  of  400,  most  astronomers  would  regard  the  night  as  a 
very  good  one ;  and  nights  on  which  a  power  of  more  than 
1000  can  be  advantageously  employed  are  quite  rare,  at  least 
in  this  climate. 

It  has  sometimes  been  said  that  Sir  William  Herschel  em- 
ployed a  power  as  high  as  6000  witli  one  of  his  great  tele- 
scopes, and,  on  the  strength  of  this,  that  the  moon  may  have 
been  brought  within  an  apparent  distance  of  forty  miles.  If 
such  a  power  was  used  on  the  moon,  we  must  suppose,  not 
merely  that  the  moon  was  seen  as  if  at  the  distance  of  forty 
miles,  even  if  Herschel  used  his  largest  telescope  —  that  of 
four  feet  aperture — but  that  the  vision  would  be  the  same  as 
if  he  had  looked  through  a  pin-hole  1^  of  an  inch  in  diam- 
eter, and  through  several  yards  of  running  water,  or  many 
miles  of  aii*.  It  is  doubtful  whether  the  moon  has  ever  been 
seen  with  any  telescope  so  well  as  it  could  be  seen  with  the 
naked  eye  at  a  distance  of  500  miles.  If  such  has  been  the 
case,  we  may  be  sure  that  the  magnifying  power  did  not  ex- 
ceed 1000. 

If  seeing  depended  entirel}'^  on  magnifying  power,  we  could 
not  hope  to  gain  much  by  further  improvement  of  the  tele- 
scope, unless  we  should  mount  our  instrument  in  some  place 
where  there  is  less  atmospheric  disturbance  than  in  the  re- 
gions where  observatories  have  hitherto  been  built.  It  is  suj)- 
posed  that,  on  the  mountains  or  table-lands  in  the  western  and 
south-western  regions  of  North  America,  the  atmosphere  is 
clear  and  steady  in  an  extraordinary  degree ;  and  if  this  sup- 
position is  entirely  correct,  a  great  gain  to  astronomy  might 
result  from  establishing  an  observatory  in  that  region. 


148  PRACTICAL  ASTRONOMY. 


CHAPTER  II. 

APPLICATION    OF   THE   TELESCOPE   TO   CELESTIAL   MEASUEEMENTa 

§  1.  Circles  of  the  Celestial  Sphere,  and  their  Relations  to  Positions 

on  the  Earth. 

Ix  the  opening  chapter  of  this  work  it  was  shown  that  all 
the  heavenly  bodies  seem  to  lie  and  move  on  the  surface  of  a 
sphere,  in  the  interior  of  which  the  earth  and  the  observer  are 
placed.  The  operations  of  Practical  Astronomy  consist  large- 
ly in  determining  the  apparent  positions  of  the  heavenly  bod- 
ies on  this  sphere.  These  positions  are  defined  in  a  way  anal- 
ogous to  that  in  which  the  position  of  a  city  or  a  ship  is  de- 
fined on  the  earth,  namely,  by  a  system  of  celestial  latitudes 
and  longitudes.  That  measure  which,  in  the  heavens,  corre- 
sponds most  nearly  to  terrestrial  longitude  is  called  Right  As- 
cension, and  that  which  corresponds  to  terrestrial  latitude  is 
called  Declination. 

In  Fig.  44  let  the  globe  be  the  celestial  sphere,  represented 
as  if  viewed  from  the  outside  by  an  observer  situated  towards 
the  east,  though  we  necessarily  see  the  actual  sphere  from  the 
centre.  Pis  the  north  pole,  ^5  the  horizon,  Q  the  south  pole 
(invisible  in  northern  latitudes  because  below  the  horizon),  EF 
the  equator,  Z  the  zenith.  The  meridian  lines  radiate  from 
the  north  pole  in  every  direction,  cross  the  equator  at  right 
angles,  and  meet  again  at  the  south  pole,  just  like  meridians 
on  the  earth.  The  meridian  from  which  right  ascensions  are 
counted,  corresponding  in  this  respect  to  the  meridian  of 
Greenwich  on  the  surface  of  the  earth,  is  that  which  passes 
through  the  vernal  equinox,  or  point  of  crossing  of  the  equa^ 
tor  and  ecliptic.    It  is  called  the  fii*st  meridian.    Three  brigb» 


CIRCLES  OF  THE  CELESTIAL  SPHERE. 


149 


stars  near  whicli  tliis  inei-idian  now  passes  may  be  seen  during 
the  autumn :  they  are  a  Andromedse  and  y  Pcgasi,  on  Maps 
11.  and  v.,  and  /3  Cassiopei^e,  on  Map  I.  The  right  ascension 
of  any  star  on  this  meridian  is  zero,  and  the  right  ascension 
of  any  other  star  is  measured  by  the  angle  wliich  the  merid- 
ian passing  through  it  makes  with  the  first  meridian,  this  angle 
being  always  counted  towards  the  east.  For  reasons  which 
will  soon  be  explained,  right  ascension  is  generally  reckoned, 
not  in  degrees,  but  in  hours,  minutes,  and  seconds  of  time. 


Fig.  44.— Circles  of  the  celestial  sphere. 


2J  is  the  ecliptic,  crossing  the  equator  at  its  point  of  inter- 
section with  the  first  meridian,  and  making  an  angle  of  23^" 
with  it.  The  declination  of  a  star  is  its  distance  from  the 
celestial  equator,  whether  north  or  south,  exactly  as  latitude 
on  the  earth  is  distance  from  the  earth's  equator.  Thus,  wlien 
the  right  ascension  and  declination  of  a  heavenly  body  are 
given,  the  astronomer  knows  its  position  in  the  celestial  sphere, 
just  as  we  know  the  position  of  a  city  on  the  earth  when  its 
longitude  and  latitude  are  given. 

It  must  be  observed  that  the  declinations  of  the  heavenly 


150  PBACTICAL  ASTRONOMY. 

bodies  are,  in  a  certain  sense,  referred  to  the  earth.  In  as- 
tronomy the  equator  is  regarded  as  a  plane  passing  tlirough 
the  centre  of  the  earth,  at  right  angles  to  its  axis,  and  dividing 
it  into  two  hemispheres.  The  line  where  this  plane  intersects 
the  surface  of  the  earth  is  our  terrestrial,  or  geographical,  equa- 
tor. If  an  observer  standing  on  the  geographical  equator  im- 
agines this  plane  running  east  and  west,  and  cutting  into  and 
through  the  earth,  where  he  stands  he  will  have  the  astro- 
nomical equator,  which  differs  from  the  geographical  equator 
only  in  being  the  plane  in  which  the  latter  is  situated.  Xow 
imagine  this  plane  continued  in  every  direction  without  limit 
till  it  cuts  the  infinite  celestial  sphere  as  in  Fig.  17,  page  62. 
The  circle  in  which  it  intersects  this  sphere  will  be  the  celes- 
tial equator.  It  will  pass  directly  over  the  head  of  the  ob- 
server at  the  equator. 

There  is  a  general  correspondence  between  latitude  on  the 
earth  and  declination  in  the  heavens,  which  may  be  seen  by 
referring  to  the  same  figure.  Here  the  reader  must  conceive 
of  the  earth  as  a  globe,  ep,  situated  in  the  centre  of  the  celes- 
tial sphere,  EPQS^  which  is  infinitely  larger  than  the  earth. 
The  plane  represented  by  EQ  is  the  astronomical  equator,  di- 
viding both  the  earth  and  the  imaginary  celestial  sphere  into 
two  equal  hemispheres.  Suppose,  now,  that  the  observer,  in- 
stead of  standing  under  the  equator,  is  standing  under  some 
other  parallel,  say  that  of  45°  Is .  (Being  in  this  latitude  means 
that  tlie  plumb-line  where  lie  stands  makes  an  angle  of  45° 
with  the  plane  of  the  equator.)  The  point  over  his  head  will 
then  be  in  45°  celestial  declination.  If  Ave  imagine  a  pencil 
of  infinite  length  rising  vertically  wliere  the  observer  stands 
80  that  its  point  shall  meet  the  celestial  sphere  in  his  zenith, 
and  if,  as  the  oartli  performs  its  diurnal  revolution  on  its  axis, 
we  imagine  this  pencil  to  leave  its  mark  on  the  celestial  sphere, 
this  mark  will  be  the  parallel  of  45°  X.  declination,  or  a  cir- 
cle everywhere  equally  distant  from  the  equator  and  from  the 
pole.  The  same  observer  will  see  tlie  celestial  pole  at  an  eleva- 
tion equal  to  his  latitude,  that  is,  at  the  angle  45°.  We  have  now 
the  following  rules  for  determining  the  latitude  of  a  place : 


CIRCLES  OF  THE  CELESTIAL  SPHERE.  151 

1.  The  latitude  is  equal  to  the  declination  of  the  observer's  zenith. 

2.  It  is  also  equal  to  the  altitude  of  the  pole  above  his  horizon. 
Hence,  if  the  astronomer  at  any  unknown  station  wishes  to 

determine  his  latitude,  he  has  only  to  find  what  parallel  of 
declination  passes  through  his  zenith,  the  latter  being  marked 
by  the  direction  of  the  plumb-line,  or  by  the  perpendicular  to 
the  surface  of  still  water  or  quicksilver.  If  he  finds  a  star 
passing  exactly  in  his  zenith,  and  knows  its  declination,  he  has 
his  latitude  at  once,  because  it  is  the  same  as  the  star's  dec- 
lination. Practically,  however,  an  observer  will  never  find  a 
known  star  exactly  in  his  zenith ;  he  must  therefore  find  at 
what  angular  distance  from  the  zenith  a  known  star  passes  his 
meridian,  and  by  adding  or  subtracting  this  distance  from  the 
star's  declination  he  has  his  latitude.  If  he  does  not  know 
the  declination  of  any  star,  he  measures  the  altitudes  above 
the  horizon  at  which  any  star  near  the  pole  passes  the  merid- 
ian, both  above  the  pole  and  under  the  pole.  The  mean  of 
the  two  gives  the  latitude. 

Let  us  now  consider  the  more  complex  problem  of  deter- 
mining longitudes.  If  the  earth  did  not  revolve,  the  obserV' 
er's  longitude  would  correspond  to  the  right  ascension  of  his 
zenith  in  the  same  fixed  manner  that  his  latitude  corresponds 
to  its  declination.  But,  owing  to  the  diurnal  motion,  there  is 
no  such  fixed  correspondence.  It  is  therefore  necessary  to 
have  some  means  of  representing  the  constantly  varying  rela- 
tion. 

Wherever  on  the  earth's  surface  an  observer  may  stand,  his 
meridian,  both  terrestrial  and  celestial,  is  represented  astronom- 
ically by  an  imaginary  plane  similar  to  the  plane  of  the  equa- 
tor. This  plane  is  vertical  to  the  observer,  and  passes  through 
the  poles.  It  divides  tlie  earth  into  two  hemispheres,  and  is 
perpendicular  to  the  equator.  In  Fig.  17,  the  celestial  and  ter- 
restrial spheres  are  supposed  to  be  cut  through  by  this  plane ; 
it  cuts  tlie  earth  when  the  observer  sta,nds  in  a  line  running 
north  and  south  from  pole  to  pole,  and  thus  forms  a  terrestrial 
meridian.  The  same  plane  intersects  the  celestial  sphere  in  a 
great  circle,  which,  rising  above  the  observer's  horizon  in  the 
H 


152  PRACTICAL  ASTRONOMY. 

north,  passes  through  the  pole  and  the  zenith,  and  disappear  at 
the  south  horizon.  Two  observers  north  and  south  of  each 
other  have  the  same  meridian ;  but  in  different  longitudes  the}* 
have  different  meridians,  which,  however,  all  pass  through  each 
pole. 

In  consequence  of  the  earth's  diurnal  motion,  the  meridian 
of  every  place  is  constantly  moving  among  the  stai*s  in  such  a 
way  as  to  make  a  complete  revolution  in  23  houi-s  56  minutes 
4.09  seconds.  The  reader  will  find  it  more  easy  to  conceive 
of  the  celestial  sphere  as  revolving  from  east  to  west,  the  ter- 
restrial meridian  remaining  at  rest ;  the  effect  being  geomet- 
rically the  same  whether  we  conceive  of  the  true  or  the  ap- 
parent motion.  There  are,  then,  two  sets  of  meridians  on 
the  celestial  sphere.  One  set  (that  represented  in  Fig.  45)  is 
fixed  among  the  stars,  and  is  in  constant  apparent  motion 
fi-om  east  to  west  with  the  stars,  while  the  other  set  is  fixed 
by  the  earth,  and  is  apparently  at  rest. 

As  differences  of  latitude  are  measured  by  angles  in  the 
heavens,  so  differences  of  terrestrial  longitude  are  measured  by 
the  time  it  takes  a  celestial  meridian  to  pass  from  one  terres- 
trial meridian  to  another ;  wliile  differences  of  right  ascension 
are  measured  by  the  time  it  takes  a  terresti'ial  meridian  to 
move  from  one  celestial  meridian  to  another.  Ordinary  solar 
time  would,  however,  be  inconvenient  for  this  measure,  because 
a  revolution  does  not  take  place  in  an  exact  number  of  hours. 
A  different  measure,  known  as  sidereal  time,  is  therefore  in- 
troduced. The  time  required  for  one  revolution  of  the  celes- 
tial meridian  is  divided  into  24  hours,  and  these  hours  are 
subdivided  into  minutes  and  seconds.  Sidereal  noon  at  any 
place  is  the  moment  at  -which  the  vernal  equinox  passes  the 
meridian  of  that  place,  and  sidereal  time  is  counted  round 
from  0  hour  to  24  honrs,  wlien  the  equinox  will  have  returned 
to  the  meridian,  and  the  count  is  commenced  over  again. 
Since  right  ascensions  in  the  heavens  are  counted  from  the 
equinox,  when  it  is  sidereal  noon,  or  0  hour,  all  celestial  ob- 
jects on  the  meridian  of  the  place  are  in  0°  of  right  ascension. 
At  1  hour  sidereal  time,  the  meridians  have  moved  15°,  and 


CIRCLES   OF  THE   CELESTIAL  SPHERE.  153 

objects  now  on  tlie  meridian  are  in  15°  of  riglit  ascension. 
Throughout  its  wliole  diurnal  course  the  right  ascension  of  the 
meridian  constantly  increases  at  the  rate  of  15°  per  hour,  so 
that  the  right  ascension  is  always  found  by  multiplying  the 
sidereal  time  by  15.  To  avoid  this  constant  multiplication,  it 
is  customary  in  astronomy  to  express  both  right  ascensions  and 
terrestrial  longitudes  by  hours.  Thus  the  Pleiades  are  said  to 
be  in  3  hours  40  minutes  right  ascension,  meaning  that  they  are 
on  the  meridian  of  any  place  at  3  hours  40  minutes  sidereal 
time.  The  longitude  of  the  Washington  Observatory  from 
Greenwich  is  77°  3';  but  in  astronomical  language  the  longi- 
tude is  said  to  be  5  hours  8  minutes  12  seconds,  meaning  that 
it  takes  5  hours  8  minutes  12  seconds  for  any  celestial  merid- 
ian to  pass  from  the  meridian  of  Greenwich  to  that  of  Wash- 
ington. In  consequence,  when  it  is  0  hour,  sidereal  time  at 
Washington,  it  is  5  hours  8  minutes  12  seconds  sidereal  time 
at  Greenwich. 

About  March  22d  of  every  year,  sidereal  0  hour  occui-s  very 
nearly  at  noon.  On  each  successive  day  it  occurs  about  3  min- 
utes 56  seconds  earlier,  which  in  the  course  of  a  year  brings 
it  back  to  noon  again.  Since  the  sidereal  time  gives  the  posi- 
tion of  the  celestial  sphere  relatively  to  the  meridian  of  any 
place,  it  is  convenient  to  know  it  in  order  to  find  what  stars 
are  on  the  meridian.  The  following  table  shows  the  sidereal 
time  of  mean,  or  ordinary  civil,  noon  at  the  beginning  of  each 
month : 

Hrs.  Min. 

July 6   38 

August 8   40 

September 10   43 

October 12   41 

November 14   43 

December 16   42 


January 18   45 

February 20   47 

March 22   37 

April 0   40 

May 2   38 

June 4   40 


The  sidereal  time  at  any  hour  of  the  year  may  be  found 
from  the  preceding  table  by  the  following  process  within  a 
very  few  minutes :  To  the  number  of  tlie  preceding  table 
corresponding  to  the  month  add  4  minutes  for  each  da}'  of 
the  month,  and  the  hour  past  noon.     The  sum  of  these  num- 


154  PRACTICAL  ASTRONOMY. 

bers,  subtracting  24  hours  if  the  sum  exceeds  that  quantity, 
will  give  the  sidereal  time.  As  an  example,  let  it  be  required 
to  find  the  sidereal  time  corresponding  to  November  13th  at 
3  A.M.     This  is  15  hours  past  noon.     So  we  have 

Hr3.    Min. 

November,  from  table 14   43 

13  daysx4 0   52 

Past  noon 15     0 

Sum 30   35 

Subtract 24     0 

Sidereal  time  required 6   35 

The  sidereal  time  obtained  in  this  way  will  seldom  or  never 
be  more  than,  five  minutes  in  error  during  the  remainder  of 
this  century.  In  every  observatory  the  principal  clock  runs 
by  sidereal  time,  so  that  by  looking  at  its  face  the  astronomer 
knows  what  stars  are  on  or  near  the  meridian.  Having  the 
sidereal  time,  the  stars  which  are  on  the  meridian  may  be 
found  by  reference  to  the  star  maps,  where  the  right  ascen- 
sions are  shown  on  the  borders  of  the  maps. 

§  2.  The  Meridian  Circle^  and  iLs  Use. 

As  a  complete  description  of  the  various  sorts  of  instru- 
ments used  in  astronomical  measurements,  and  of  the  modes 
of  using  them,  would  interest  but  a  small  class  of  readei-s, 
we  shall  confine  ourselves  for  the  present  to  one  which  may 
be  called  the  fundamental  instrument  of  modern  astronomy, 
the  application  of  which  has  direct  and  immediate  reference 
to  the  circles  of  the  celestial  sphere  described  in  the  preceding 
section.  This  one  is  termed  the  Meridian  Circle,  or  Transit  Cir- 
cle. Its  essential  parts  are  a  moderate-sized  telescope  balanced 
on  an  axis  passing  through  its  centre,  with  a  system  of  fine 
lines  in  the  eye-piece ;  one  or  two  circles  fastened  on  the  axis, 
revolving  with  the  telescope,  and  having  degrees  and  subdi- 
visions cut  on  their  outer  edges;  and  a  set  of  microscope  mi- 
crometers for  measuring  between  the  lines  so  cut.  It  is  abso- 
lutely necessary  that  every  part  of  the  instrument  shall  be  of 
the  most  perfect  workmanship,  and  that  the  masonry  piers  on 


TRE  MERIDIAN  CIRCLE,  AND  ITS   USE. 


155 


which  it  is  mounted  shall  be  as  stable  as  it  is  possible  to  make 
them. 

There  are  many  differences  of  detail  in  the  construction 
and  mounting  of  different  meridian  circles,  but  they  all  turn 
on  an  east  and  west  horizontal  axis,  and  therefore  the  telescope 
moves  only  in  the  plane  of  the  meridian.     Fig.  45  shows  the 


Fig.  45.— The  Washingtou  transit  circle. 

construction  of  the  great  circle  in  the  Naval  Observatory, 
Washington.  The  marble  piers,  PP,  are  supported  on  a  mass 
of  masonry  under  the  floor,  the  bottom  of  which  is  twelve  feet 
below  the  surface  of  the  ground.  The  middle  of  the  telescope 
is  formed  of  a  large  cube,  about  fifteen  inches  on  each  side. 
From  the  east  and  west  side  of  this  cube  extend  the  trunn- 
ions, which  are  so  large  next  the  cube  as  to  be  nearly  conical 
in  shape.  The  outer  ends  terminate  in  fiuely  ground  steel 
pivots  two  and  a  half  inches  in  diameter,  which  rest  on  brass 
Vs  firmly  fixed  to  heavy  castings  set  into  the  piers  with  hy- 


156 


PRACTICAL  ASTRONOMY. 


draulic  cement.  In  order  that  the  delicate  pivots  may  not 
be  worn  by  the  whole  weight  of  the  instrument  resting  on 
them,  the  counterpoises,  BB,  support  all  the  weight  except  30 
or  40  pounds.  Near  the  ends  of  the  axis  are  the  circles,  seen 
edgewise,  which  are  firmly  screwed  on  the  trunnions,  and  there- 
fore turn  with  the  instrument.  Each  pier  carries  four  arms, 
and  each  of  these  arms  carries  a  microscope,  marked  ni,  hav- 
ina:  in  its  focus  the  face  of  the  circle  on  which  the  lines  are 
cut.  These  lines  divide  the  circle  into  360°,  and  each  degree 
into  thirty  spaces  of  two  minutes  each,  so  that  there  are  10,800 
lines  cut  on  the  circle.  They  are  cut  in  a  silver  band,  and  are 
so  fine  as  to  be  invisible  to  the  naked  eye  unless  the  light  is 
thrown  upon  them  in  a  particular  way.  On  each  side  of  the 
instrument,  in  a  line  with  the  axis,  is  a  lamp  which  throws 
light  into  the  telescope  so  as  to  illuminate  the  field  of  view. 
Reflecting  prisms  inside  of  the  pier  throw  some  of  the  light 
upon  those  points  of  the  circle  which  are  viewed  by  the  mi- 
croscopes, so  as  to  illuminate  the  fine  divisions  on  the  circle. 
Being  thus  limited  in  its  movements,  an  object  can  be  seen 
with  the  telescope  only  when  on,  or  very  near,  tlie  meridian. 
The  sole  use  of  the  instrument  is  to  observe  the  exact  times 
at  which  stars  cross  the  meridian,  and  their  altitudes  above 
the  horizon,  or  distances  from  the  zenith,  at  the  time  of  cross- 
ing. To  give  precision  to  these  observations,  the  eye-piece  of 
the  instrument  is  supplied  with  a  system  of  fine  black  lines, 

usually  made  of  spider's  web,  as 
shown  in  Fig.  46.  These  lines 
are  set  in  the  focus,  so  that  the 
image  of  a  star  crossing  the  me- 
ridian passes  over  them.  The 
middle  vertical  spider  line  marks 
the  meridian ;  and  to  find  the 
time  of  meridian  transit  of  a  star 
it  is  only  necessary  to  note  the 
moment  of  passage  of  its  image 
„    ,.    c    1    r     ■  «,,  f  •    "f    over  this  line.    But,  to  give  great- 

Fio.  4G.— Spider  lines  in  Held  of  view  of  ^  '         o  &         ^ 

a  meridian  circle.  er  precision  and  Certainty  to  his 


THE  MEBIDIAN  CIRCLE,  AND  ITS    USE.  157 

observation,  the  astronomer  generally  notes  the  moments  of 
transit  over  five  or  more  lines,  and  takes  the  average  of  them 
all. 

Formerly  the  astronomer  had  to  find  the  times  of  transit  by 
listening  to  the  beat  of  his  sidereal  dock,  counting  the  sec- 
onds, and  estimating  the  tenths  of  a  second  at  which  the  tran- 
sit over  a  line  took  place.  If,  for  instance,  he  should  find  that 
the  star  had  not  reached  the  line  when  the  tick  of  twenty- 
three  seconds  was  heard,  but  crossed  before  the  twenty-fourth 
second  was  ticked,  he  would  know  that  the  time  was  twenty- 
three  seconds  and  some  fraction,  and  would  have  to  estimate 
what  that  fraction  was.  A  skilful  observer  will  generally 
make  this  estimate  within  a  tenth  of  a  second,  and  will  only 
on  rare  occasions  be  in  error  by  as  much  as  two  tenths. 

Shortly  after  the  introduction  of  the  electric-telegraph,  the 
American  astronomers  of  that  day  introduced  a  much  easier 
method  of  determining  the  time  of  transit  of  a  star,  by  means 
of  the  eleciro-chro7iograph.  As  now  made,  this  instrument  con- 
sists of  a  revolving  cylinder,  having  a  sheet  of  paper  wrapped 
around  it,  and  making  one  revolution  per  minute.  A  pen 
or  other  marker  is  connected  with  a  telegraphic  apparatus  in 
such  a  way  that  whenever  a  signal  is  sent  to  the  pen  it  makes 
a  mark  on  the  moving  paper.  This  pen  moves  lengthwise  of 
the  cylinder  at  the  rate  of  about  an  inch  in  ten  minutes,  so 
that,  in  consequence  of  the  turning  of  the  cylinder  on  its  axis, 
the  marks  of  the  pen  will  be  along  a  spiral,  the  folds  of  which 
are  one-tenth  of  an  inch  apart.  The  galvanic  circuit  which 
works  tlie  pen  is  connected  with  the  sidereal  clock,  so  that  the 
latter  causes  tlie  pen  to  make  a  signal  every  second.  The 
same  pen  may  be  worked  by  a  telegraphic  key  in  the  hand 
of  the  observer.  The  latter,  looking  into  his  telescope,  and 
watching  the  approach  of  the  image  of  the  star  to  each  wire, 
makes  a  signal  at  the  moment  at  wliich  the  star  crosses.  This 
signal  is  recorded  on  the  chronograph  in  its  proper  place 
among  the  clock  signals,  from  which  it  may  be  distinguished 
by  its  greater  strength.  The  record  is  permanent,  and  the 
sheet  may  be  taken  oif  and  read  at  leisure,  the  exact  tenth  of 


158  PRACTICAL  ASTRONOMY. 

a  second  at  which  each  signal  was  made  being  seen  by  its 
position  among  the  clock  signals.  The  great  advantages  of 
this  method  are,  that  great  skill  and  practice  are  not  required 
to  make  good  observations,  and  that  the  observer  need  not  see 
either  the  clock  or  his  book,  and  can  make  a  great  number  of 
observations  in  the  course  of  the  evening  which  may  be  read 
off  at  leisure.  In  the  case  of  the  most  skilful  observers  there 
is  no  great  gain  in  accuracy,  for  the  reason  that  they  can  esti- 
mate the  fraction  of  a  second  by  the  eye  and  ear  with  nearly 
the  same  accuracy  that  they  can  give  the  signal. 

The  zenith  distance  of  the  star,  from  which  its  declination 
is  determined,  is  observed  by  having  in  the  reticule  a  hori- 
zontal spider  line  which  is  made  to  bisect  tlie  image  of  the 
star  as  it  passes  the  meridian  line.  The  observer  then  goes  to 
the  microscopes,  ascertains  what  lines  cut  on  the  circle  are  un- 
der them,  and  what  number  of  seconds  the  nearest  line  is  from 
the  proper  point  in  the  field  of  the  microscope.  Tlie  mean  of 
the  results  from  the  four  microscopes  is  called  the  circle-reading ^ 
and  can  be  determined  within  two  or  three  tenths  of  a  second 
of  arc,  or  even  nearer,  if  all  the  apparatus  is  in  the  best  order. 
The  minuteness  of  this  angle  may  be  judged  by  the  circum- 
stance that  the  smallest  round  object  a  keen  eye  can  see  sub- 
tends an  angle  of  about  forty  seconds. 

We  have  described  only  the  leading  operations  necessary  in 
determinations  with  a  meridian  circle.  To  complete  the  de- 
termination of  the  position  of  a  star  as  accuratel}'  as  a  prac- 
tised observer  can  bisect  it  with  the  spider  line  is  a  much  more 
complicated  matter,  owing  to  the  unavoidable  errors  and  im- 
perfections of  his  instrument.  It  is  impossible  to  set  the  lat- 
ter in  the  meridian  with  mathematical  precision,  and,  if  it  were 
done,  it  would  not  remain  so  a  single  day.  When  the  astron- 
omer comes  to  tenths  of  seconds,  he  has  difficulties  to  contend 
with  at  every  step.  Tlie  effects  of  changes  of  temperature 
and  motions  of  the  solid  earth  on  the  foundations  of  his  in- 
strument are  such  as  to  keep  it  constantly  changing ;  his  clock 
is  so  far  from  going  right  that  he  never  attempts  to  set  it  per- 
fectly right,  but  only  determines  its  error  from  his  observa- 


DETERMINATION  OF  TERRESTRIAL  LONGITUDES.      159 

tions.  Every  observation  must,  therefore,  be  corrected  for  a 
number  of  instrumental  errors  before  the  result  is  accurate, 
an  operation  many  times  more  laborious  than  merely  making 
the  observation. 

§  3.  Determination  of  Terrestrial  Longitudes. 

The  telegraphic  mode  of  recording  observations,  described 
in  the  last  section,  affords  a  method  of  determining  differences 
of  longitude  between  places  connected  by  telegraph  of  ex- 
traordinary elegance  and  perfection.  AVe  have  already  shown 
that  the  difference  of  longitude  between  two  points  is  meas- 
ured by  the  time  it  takes  a  star  to  move  from  the  meridian  of 
the  easternmost  point  to  that  of  the  westernmost  point.  We 
have  also  explained  in  the  last  section  how  an  observer  with  a 
meridian  circle  determines  and  records  the  passage  of  a  star 
over  his  meridian  within  a  tenth  of  a  second.  Since  the  ze- 
nith distance  of  the  star  is  not  required  in  this  observation,  the 
circles  and  microscopes  may  be  dispensed  with,  and  the  instru^ 
ment  is  then  much  simpler  in  construction,  and  is  termed  a 
Transit  Instrument.  When  the  observer  makes  a  telegraphic 
record  of  the  moment  of  transit  of  a  star  by  striking  a  key  in 
the  manner  described,  it  is  evident  that  the  electro -chrono- 
graph on  which  his  taps  are  recorded  may  be  at  any  distance 
to  which  the  electric  current  can  carry  his  signal.  It  may, 
therefore,  be  in  a  distant  city.  There  is  no  difficulty  in  a 
Washington  observer  recoi'ding  his  observations  in  Cincinnati. 

On  this  system,  the  mode  of  operation  is  about  as  follows : 
die  Washington  and  Cincinnati  stations  eacli  lias  its  transit  in- 
strument, its  observer,  and  its  chronograph ;  but  the  chrono- 
graphs are  connected  by  telegraph,  so  that  any  signal  luaJc 
by  either  observer  is  recorded  on  both  chronograplis.  As 
the  Washington  observer  sees  a  star  previously  agreed  on  pass 
over  the  lines  in  tlie  focus  of  liis  instrument,  he  makes  sig- 
nals with  his  telegraphic  key,  wliich  are  recorded  both  on  his 
own  clironograph  and  on  that  of  Cincinnati.  When  the  star 
reacb.es  the  meridian  of  the  latter  city,  the  observer  there  sig- 
nals the  transit  of  the  star  in  like  manner,  and  the  momont 

12 


160  PRACTICAL  ASTEONOMY. 

of  passage  over  each  line  in  the  focus  of  his  instrument  is 
recorded,  both  in  Cincinnati  and  "Washington.  The  elapsed 
time  is  then  found  by  measuring  off  the  chronograph  sheets. 

The  reason  for  having  all  the  observations  recorded  on  both 
chronographs  is  that  the  results  may  be  corrected  for  the  time 
it  takes  the  electric  current  to  pass  betvreen  the  two  cities, 
which  is  quite  perceptible  at  great  distances.  In  consequence 
of  this  "  wave-time,"  the  Washington  observation  will  be  re- 
corded a  little  too  late  at  Cincinnati,  so  that  the  difference  of 
longitude  on  the  Cincinnati  chronograph  will  be  too  small. 
The  Cincinnati  observation,  which  comes  last,  being  recorded 
a  little  too  late  at  Washington,  the  difference  of  time  on  the 
Washington  chronograph  will  be  a  little  too  great.  The  mean 
of  the  2"e3ults  on  the  two  chronographs  will  be  the  correct 
longitude,  while  their  difference  will  be  twice  the  time  it  takes 
the  electric  current  to  pass  between  the  two  cities.  The  re- 
sults thus  obtained  for  the  velocity  of  electricity  are  by  no 
means  accordant,  but  the  larger  number  do  not  differ  very 
greatly  from  SOOO  miles  per  second. 

A  celestial  meridian  moves  over  the  earth's  surface  at  the 
rate  of  fifteen  degrees  an  hour,  or  a  minute  of  arc  in  four  sec- 
onds of  time.  More  precisely,  this  is  the  rate  of  rotation  of 
the  earth.  The  length  of  a  minute  of  arc  in  longitude  de- 
pends on  the  latitude.  It  is  about  6000  feet,  or  a  mile  and  a 
sixth  at  the  equator,  but  diminishes  whether  we  go  north  or 
south,  owing  to  the  approach  of  the  meridians  on  the  globular 
earth,  as  can  be  seen  on  a  globe.  In  the  latitude  of  our  Mid- 
dle States  it  is  about  4600  feet,  so  that  the  surface  of  the  earth 
there  moves  over  1150  feet  a  second.  At  the  latitude  of 
Greenwich  it  is  3S00  feet,  so  that  the  motion  is  950  feet  per 
second.  Two  skilful  astronomei"s,  by  making  a  great  num- 
ber of  observations,  can  determine  the  time  it  takes  the  stai'S 
to  pass  from  one  meridian  to  another  within  one  or  two  hun- 
dredths of  a  second  of  time,  and  can  therefore  make  sure  of 
the  difference  of  longitude  between  two  distant  cities  within 
six  or  eight  yards. 

Of  late  the  telegraphic  method  of  determining  longitudes 


DETERMINATION  OF  TERRESTRIAL  LONGITUDES.     161 

has  been  applied  in  a  way  a  little  different,  though  resting  on 
the  same  principles.  Instead  of  recording  the  transits  of  stars 
on  both  chronographs,  each  observer  determines  the  error  of 
his  clock  by  transits  of  stars  of  which  the  right  ascension  has 
been  carefully  determined.  Each  clock  is  then  connected  witli 
both  chronographs  by  means  of  the  telegraphic  lines,  and  made 
to  record  its  beats  for  the  space  of  a  few  minutes  only.  Thus 
the  difference  between  the  sidereal  times  at  the  two  stations 
for  the  same  moment  of  absolute  time  can  be  found,  and  this 
difference  is  the  difference  of  longitude  in  time.  A  few  years 
ago,  when  the  difference  of  longitude  between  points  on  the 
Atlantic  and  Pacific  coasts  was  determined  by  the  Coast 
Survey,  a  clock  in  Cambridge  was  made  to  record  its  beats  on 
a  chronograph  in  San  Francisco,  and  vice  versa.  In  1866,  as 
soon  as  the  Atlantic  cable  had  been  successfully  laid,  Dr.  B.  A. 
Gould  went  to  Europe,  under  the  auspices  of  the  Coast  Su.rvey, 
to  determine  the  difference  of  longitude  between  Europe  and 
America.  Owing  to  the  astronomical  importance  of  this  de- 
termination, it  has  since  been  twice  repeated,  once  under  the 
direction  of  Mr.  Dean,  and,  lastly,  under  that  of  Mr.  Ililgard, 
both  of  the  Survey.  These  three  campaigns  gave  the  follow- 
ing separate  results  for  the  difference  of  longitude  between 
the  Royal  Observatory,  Greenwich,  and  the  Naval  Observato- 
ry, Washington : 

Hr3.  Min.      Sec. 

Dr.  Gould,  1867 5     8     12.11 

Mr.  Dean,  1870 5     8     12.16 

Mr.  Hilgaid,  1872 5    8     12.09 

The  extreme  difference,  it  will  be  seen,  is  less  than  a  tenth  of 
a  second,  and  would  probably  have  been  smaller  but  for  the 
numerous  difficulties  attendant  on  a  determination  through  a 
long  ocean  cable,  which  are  much  greater  than  through  a  land 
line. 

The  use  of  the  telegraph  for  the  determination  of  longitude 
is  necessarily  limited,  and  other  methods  must  therefore  gen- 
erally be  used.  The  general  problem  of  determining  a  longi- 
tude, whether  that  of  a  ship  upon  the  ocean  or  of  a  station 


162  PRACTICAL  ASTRONOMY. 

upon  the  land,  depends  on  two  requirements :  (1)  a  knowledge 
of  the  local  time  at  the  station,  and  (2)  a  knowledge  of  the 
corresponding  time  at  Greenwich,  Washington,  or  some  other 
standard  meridian.  The  difference  of  these  two  represents 
the  longitude. 

The  first  determination,  that  of  the  local  time,  is  not  a  diffi- 
cult problem  when  the  utmost  accuracy  is  not  required.  We 
have  alread}'  shown  how  it  is  determined  with  a  transit  instru- 
ment. But  this  instrument  cannot  be  used  at  all  at  sea,  and 
is  someM'hat  heavy  to  carry  and  troublesome  to  set  up  on  the 
land.  For  ships  and  travellers  it  is,  therefore,  much  more  con- 
venient to  use  a  sextant,  by  which  the  altitude  of  the  sun  or  of 
a  star  above  the  horizon  can  be  measured  with  very  little  time 
or  trouble.  To  obtain  the  time,  the  observation  is  made,  not 
when  the  object  is  on  the  meridian,  but  when  it  is  as  nearly  as 
practicable  east  or  west.  Having  found  the  altitude,  the  calcu- 
lation of  a  spherical  triangle  from  the  data  given  in  the  Nau- 
tical Almanac  at  once  gives  the  local  time,  or  the  ei-ror  of  the 
chronometer  on  local  time. 

Tlie  difficult  problem  is  to  determine  the  Greenwich  time. 
So  necessary  to  navigation  is  some  method  of  doing  this,  that 
the  British  Government  long  had  a  standing  offer  of  a  reward 
of  £10,000  to  any  one  who  would  find  a  successful  method 
of  determining  the  longitude  at  sea.  When  the  office  of  As- 
tronomer Boj'al  was  established,  which  was  in  1675,  the  duty 
of  the  incumbent  was  declared  to  bo  "to  apply  himself  Avith 
the  most  exact  care  and  diligence  to  the  rectifj'ing  the  Ta- 
bles of  the  Motions  of  the  Heavens,  and  the  places  of  the 
Fixed  Stars,  in  order  to  find  out  the  so  much  desired  Longi- 
tude at  Sea  for  the  perfecting  the  Art  of  Navigation. ''  The 
reward  above  referi-ed  to  was  ultimately  divided  between  an 
astronomer,  Tobias  Mayer,  who  made  a  great  improvement  in 
the  tables  of  the  moon,  and  a  watch-maker  who  improved  the 
marine  chronometer. 

Tlie  moon,  making  her  monthly  circuit  of  the  heavens,  may 
be  considered  a  sort  of  standard  clock  from  which  the  astron- 
omer can  learn  the  Greenwich  time,  in  whatever  part  of  the 


DETERMINATION  OF  TERRESTRIAL  LONGITUDES.      163 

world  he  may  find  himself.  This  he  does  by  observing  her  po- 
sitions among  the  stars.  The  Nautical  Almanac  gives  the  pre- 
dicted distance  of  the  moon  from  certain  other  bodies — sun, 
planets  or  bright  stars — for  every  three  hours  of  Greenwich 
time ;  and  if  the  astronomer  or  navigator  measures  this  dis- 
tance with  a  sextant,  he  has  tlie  means  of  finding  at  what 
Greenwich  time  the  distance  was  equal  to  that  measured.  Un- 
fortunately, however,  this  operation  is  much  like  that  of  deter- 
mining the  time  from  a  clock  which  has  nothing  but  an  liour- 
hand.  The  moon  moves  among  the  stars  only  about  13°  in 
a  day,  and  her  own  diameter  in  an  hour.  If  the  observer  wants 
his  Greenwich  time  within  half  a  minute,  he  must  determine 
the  position  of  the  moon  within  tlie  hundred  and  twentieth  of 
her  diameter.  This  is  about  as  near  as  an  ordinary  observer 
at  sea  can  come  with  a  sextant ;  and  yet  the  error  would  be  7-| 
miles  of  longitude.  Even  this  degree  of  exactness  can  be  ob- 
tained only  by  having  tlie  moon's  place  relatively  to  the  stars 
predicted  with  great  accuracy;  and  here  we  meet  with  one  of 
the  most  complex  problems  of  astronomy,  the  efforts  to  solve 
which  have  already  been  mentioned. 

In  addition  to  the  uncertainty  of  which  we  have  spoken, 
this  method  is  open  to  the  objection  of  being  difficult,  owing 
to  the  long  calculation  necessary  to  free  the  measured  distance 
from  the  effects  of  the  refraction  of  both  bodies  by  the  atmos- 
phere, and  of  the  parallax  of  the  moon.  On  ordinary  voyages 
navigators  prefer  to  trust  to  their  chronometers.  The  error  of 
the  chronometer  on  Greenwich  time  and  its  daily  rate  are 
determined  at  ports  of  which  the  longitude  is  known,  and  the 
navigator  can  then  calculate  this  error  on  the  supposition  that 
the  chronometer  gains  or  loses  the  same  amount  every  day. 
On  voyages  between  Europe  and  America  a  good  chronome- 
ter will  not  generally  deviate  more  than  ten  or  fifteen  seconds 
from  its  calculated  rate,  so  that  it  answers  all  the  purposes  of 
navigation. 

Still  another  observation  by  which  Greenwich  time  may  be 
obtained  to  a  minute  in  any  part  of  the  world  is  that  of  the 
eclipses  of  Jupiter's  first  satellite.     The  Greenwich  or  Wash- 


164  PBACTICAL  ASTEOXOMY. 

iugton  times  at  which  the  eclipses  are  to  occur  are  given  in 
the  Xautical  Almanac,  so  that  if  the  traveller  can  succeed  in 
observing  one.  he  has  his  Greenwich  time  at  once,  without  any 
calculation  whatever.  But  the  error  of  his  observation  may 
be  half  a  minute,  or  even  an  entire  minute,  so  that  this  meth' 
od  is  not  at  all  accurate. 

"Where  an  astronomer  can  fit  up  a  portable  observatory,  the 
observation  of  the  moon  affords  him  a  much  more  accurate 
longitude  than  it  does  the  navigator,  because  he  can  use  better 
instruments.  If  he  has  a  transit  instrument,  he  determines 
from  observation  the  right  ascension  of  the  moon's  limb  as 
she  passes  his  meridian,  and  then,  referring  to  the  Nautical 
Almanac,  he  finds  at  what  Greenwich  time  the  limb  had  this 
right  ascension.  A  single  transit  would,  if  the  moon's  place 
were  correctly  predicted,  give  a  longitude  correct  within  six 
or  eight  seconds  of  time.  It  is  found,  however,  that,  owing  to 
the  errors  of  the  moon's  tables,  it  is  necessary  for  the  astron- 
omer to  wait  for  corresponding  observations  of  the  moon  at 
some  standard  observatory  before  he  can  be  sure  of  this  de- 
gree of  accuracy. 

§  -i.  Mean,  or  Cloch^  Time. 

We  have  hitherto  described  only  sidereal  time,  which  corre- 
sponds to  the  diurnal  revolution  of  the  starry  sphere,  or,  more 
exactly  yet,  of  the  vernal  equinox.  Sucli  a  measure  of  time 
would  not  answer  the  purposes  of  civil  life,  and  even  in  astron- 
omy its  use  is  generally  confined  to  the  determination  of  right 
ascensions.  Solar  time,  regulated  by  the  diurnal  motion  of  the 
sun,  is  almost  universally  used  in  astronomical  observations  as 
well  as  in  civil  life.  Formerly,  solar  time  was  made  to  con- 
form absolutely  to  the  motion  of  the  sun  ;  that  is,  it  was  noon 
when  the  sun  was  on  the  meridian,  and  the  hours  were  those 
that  would  be  given  by  a  sundial.  If  the  interval  between 
two  consecutive  transits  of  the  sun  were  always  the  same, 
this  measure  would  have  been  adhered  to.  But  there  are  two 
sources  of  variation  in  the  motion  of  the  sun  in  right  ascen- 
sion, the  effect  of  which  is  to  make  these  intervals  unequal : 


MEAN,  OB   CLOCK,  TIME.  165 

1.  The  eccentricity  of  the  earth's  orbit.  In  consequence 
of  tliis,  ac  ah-eady  explained,  the  angular  motion  of  the  earth 
round  the  sun  is  more  rapid  in  December,  when  the  earth  is 
nearest  the  sun,  than  in  June,  when  it  is  farthest.  The  aver- 
age, or  mean,  motion  is  such  that  the  sun  is  3  minutes  50  sec- 
onds longer  in  returning  to  the  meridian  than  a  star  is.  But, 
owing  to  the  eccentricity,  this  motion  is  actually  one-thirtietii 
greater  in  December,  and  the  same  amount  less  in  June ;  so 
that  it  varies  from  3  minutes  48  seconds  to  4  minutes  4  sec- 
onds. 

2.  The  principal  source  of  the  inequality  referred  to  is  the 
obliquity  of  the  ecliptic.  When  the  sun  is  near  tlie  equinoxes, 
his  motion  among  the  stars  is  oblique  to  the  direction  of  the 
diurnal  motion;  while  the  latter  motion  is  directly  to  the 
west,  the  former  is  23|^°  north  or  south  of  east.  If,  then,  sun 
and  star  cross  the  meridian  together  one  day  near  the  equinox, 
'le  will  not  be  3  minutes  56  seconds  later  than  the  star  in 
crossing  the  next  day,  but  about  one -twelfth  less,  or  20  sec- 
onds. Therefore,  at  the  times  of  the  equinoxes,  the  solar  days 
are  about  20  seconds  shorter  than  the  average.  At  the  sol- 
stices, the  opposite  effect  is  produced.  The  sun,  being  23|^° 
nearer  the  pole  than  before,  the  diurnal  motion  is  slower,  and 
it  takes  the  sun  20  seconds  longer  than  the  regular  interval  of 
3  minutes  56  seconds  for  that  motion  to  carry  the  sun  over 
ihe  space  which  separates  him  from  the  star  w'hich  culminat- 
ed with  him  the  day  before.  The  days  are  then  20  seconds 
longer  than  the  average,  from  this  cause. 

So  long  as  clocks  could  not  be  made  to  keep  time  within 
20  seconds  a  day,  these  variations  in  the  course  of  the  sun 
were  not  found  to  cause  any  serious  inconvenience.  But 
when  clocks  began  to  keep  time  better  than  the  sun,  it  be- 
came necessary  either  to  keep  putting  them  ahead  when  tiie 
sun  went  too  fast,  and  behind  when  he  M'ent  too  slow,  or  to 
give  up  the  attempt  to  make  them  correspond.  The  latter 
course  is  now  universally  adopted,  where  accurate  time  is  re- 
quired ;  the  standard  sun  for  time  being,  not  the  real  sun,  but 
a  "  mean  sun,"  which  is  sometimes  ahead  of  the  real  one.  and 


166  PRACTICAL  ASTRONOMY. 

sometimes  behind  it.  The  irregular  time  depending  on  the 
motion  of  the  true  sun,  or  that  given  by  a  sundial,  is  called 
Apparent  Time,  while  that  given  by  the  mean  sun,  or  by  a 
clock  going  at  a  uniform  rate,  is  called  Mean  Time.  The  two 
measures  coincide  four  times  in  a  year;  during  two  interme- 
diate seasons  the  mean  time  is  ahead,  and  during  two  it  is 
behind.  The  following  are  the  dates  of  coincidence,  and  of 
maximum  deviation,  which  vary  but  slightly  from  year  to 
year : 

February  10th True  sun  15  minutes  slow. 

April  loth "  "  correct. 

May  14tii "  ''  4  minutes  fast. 

June  14th "  '•  coiTect. 

July  25th "  "  6  minutes  slow. 

August  31st "  "  correct. 

November  2d "  "  16  minutes  fast. 

December  24th "  "  correct. 

"Wlien  the  sun  is  slow,  it  passes  the  meridian  after  mean  noon, 
and  the  clock  is  faster  than  the  sundial,  and  vice  versa.  These 
wide  deviations  are  the  result  of  the  gradual  accumulations  of 
the  deviations  of  a  few  seconds  from  day  to  day,  the  cause  of 
which  has  just  been  explained.  Thus,  during  the  interval  be- 
tween November  2d  and  February  12th,  the  sun  is  constantly 
falling  behind  the  clock  at  an  avei-age  rate  of  18  or  19  seconds 
a  day,  which,  continued  through  100  days,  brings  it  from  16 
minutes  fast  to  15  minutes  slow. 

This  difference  between  the  real  and  the  mean  sun  is  called 
the  Equation  of  Time.  One  of  its  effects,  which  is  frequently 
misunderstood,  is  that  the  interval  from  sunrise  until  noon,  as 
given  in  the  almanacs,  is  not  the  same  as  that  between  noon 
and  sunset.  This  often  leads  to  the  inquiry  whether  the  fore- 
noons can  be  longer  or  shorter  than  the  afternoons.  If  by 
"  noon  "  we  meant  the  passage  of  the  real  sun  across  the  me- 
ridian, they  could  not :  but  the  noon  of  our  clocks  being  some- 
times 15  minutes  before  or  after  noon  by  the  sun,  the  former 
may  be  half  an  hour  nearer  to  sunrise  than  to  sunset,  or  vice 
versa. 


PARALLAX  IN  GENERAL.  167 


CHAPTER  III. 

MEASURING   DISTANCES    IN    THE   HEAVENS. 

§  1.  Parallax  in  General. 

The  determination  of  the  distances  of  the  heavenly  bodies 
from  ns  is  a  much  more  complex  problem  than  merely  deter- 
mining their  apparent  positions  on  the  celestial  sphere.  The 
latter  depend  entirely  on  the  direction  of  the  bodies  from  the 
observer ;  and  two  bodies  which  lie  in  the  same  direction  will 
seem  to  occupy  the  same  position,  no  matter  how  much  farther 
one  may  be  than  the  other.  Notwithstanding  the  enormous 
differences  between  the  distances  of  different  heavenly  bodies, 
there  is  no  way  of  telling  even  which  is  farthest  and  which 
nearest  by  mere  inspection,  much  less  can  the  absolute  dis- 
tance be  determined  in  this  way. 

The  distances  of  the  heavenly  bodies  are  generally  deter- 
mined from  their  Parallax.  Pai'allax  may  be  defined,  in  the 
most  general  way,  as  the  difference  betiveen  the  ^/^ 

directions  of  a  body  as  seen  from  two  different  f^ 

points.     Other  conditions   being  equal,  the  l^)A 

more  distant  the  bodv,  the  less   this  differ-  /  /  \  \ 

ence,  or  the  less  the  parallax.     To  show,  in  I  /      \\ 

the  most  elementary  way,  how  difference  of        //  \\ 

direction  depends   on   distance,  suppose   an       //  \\ 

observer  at  0  to  see  two  lights,  A  and  B,  at     •/  \ 

night.     He  cannot  tell  by  mere   inspection    /o  A 

which  is  the  more  distant.     But  suppose  he  fig. 47.— Diagram  iiins. 
walks  over  to  the  point  P.     Both  lights  will       '''^'"'s  p'"'^""^- 
then  seem  to  change  their  direction,  moving  in  the  direction 
opposite  to  that  in  which  he  goes.    But  the  light  .4  will  change 
more  than  the  light  B,  for,  being  to  the  right  of  B  when  the 


IGS 


PRACTICAL  ASTRONOMY. 


observer  was  at  0,  it  is  now  to  the  left  of  it.     The  observei 
ean  then  say  with  entire  certainty  that  A  is  nearer  than  B. 

As  a  steamship  crosses  the  ocean,  near  objects  at  rest 
change  tlieir  direction  rapidly,  and  soon  flit  b}',  while  more 
distant  ones  cliange  very  slowly.  The  stai-s  are  not  seen  to 
change  at  all.  If,  however,  the  moon  did  not  move,  the  pas- 
senger would  see  her  to  have  changed  her  apparent  position? 
about  one  and  a  half  times  her  diameter  in  consequence  of 
the  journey.  If,  when  the  moon  is  near  the  meridian,  an  ob- 
server could  in  a  moment  jump  from  Xew  York  to  Liverpool, 
keeping  his  eye  fixed  upon  her,  he  would  see  her  apparently 
jump  in  tlie  opposite  direction  about  this  amount. 

Astronomically,  the  direction  of  an  object  from  an  observer 
is  determined  by  its  position  on  the  celestial  sphere ;  that  is, 
by  its  right  ascension  and  declination.  In  consequence  of 
parallax,  the  declination  of  a  body  is  not  the  same  when  seen 
from  different  parts  of  the  earth.  As  the  moon  passes  the 
meridian  of  the  Cape  of  Good  Hope,  her  measured  declina- 
tion may  be  a  degree  or  more  farther  north  than  it  is  when 
she  passes  the  meridian  of  Greenwich.  The  determination  of 
the  parallax  of  the  moon  was  one  of  the  objects  of  the  British 
Government  in  establishing  an  observatory  at  the  Cape,  and 
so  well  has  this  object  been  attained  that  the  best  determina- 
tions of  the  parallax  have  been  made  by  comparing  the  Green- 
wich and  Cape  observations  of  the  moon's  declination. 

The  determination  of  the  distance  of  a  celestial  object  from 
the  parallax  depends  on  the  solution  of  a  triangle.  If,  in  Fig. 
48,  we  suppose  the  circle  to  represent  the  earth,  and  imagine 

an  observer  at  A  to  view  a  celes- 
tial object,  J/,  he  will  see  it  pro- 
jected on  the  infinite  celestial 
sphere  in  the  direction  AM  con- 
tinued. Another  observer  at  A' 
will  see  it  in  the  direction  A'Jf. 
The  difference  of  these  directions 
is  the  angle  at  M.  Knowing  all 
Fio.  4S.— Diagram  iiinstrating  parallax,  the   angles    of  the   quadrilateral 


PARALLAX  IN  GENERAL. 


169 


ACA'M,  and  the  length  of  the  earth's  radius,  CA,  the  dis- 
tance of  the  object  from  the  three  points,  A,  A',  and  C,  can 
be  found  by  solving  a  simple  problem  of  trigonometry. 

The  term  ji'^^^^^'^^  is  frequently  used  in  a  more  limited 
sense  than  that  in  which  we  have  just  defined  and  elucidated 
it.  Instead  of  the  difference  of  directions  of  a  celestial  body 
seen  from  any  two  points,  the  astronomer  generally  means  the 
difference  between  the  direction 
of  the  body  as  it  would  appear 
from  the  centre  of  the  earth,  and 
the  direction  seen  by  an  observer 
at  the  surface.  Thus,  in  Fig.  49, 
an  observer  at  the  centre  of  the 
earth,  C,  would  see  the  object  M' 
in  the  dii'cction  CJ/',  while  one 
on  the  surface  at  P  will  see  it  in 
the  direction  PM'.  The  differ- 
ence   of    tliese    directions    is    the  Fig.  49.— variation  of  parallax  with  the 

angle   PM'C.     If  the   observer  "'"'"^*^- 

should  be  at  the  point  where  the  line  M'C  intersects  the  sur- 
face of  the  earth,  there  would  be  no  parallax :  in  this  case, 
the  object  would  be  in  his  geocentric  zenith.  If,  on  the  other 
hand,  the  observer  has  the  object  in  his  horizon,  so  tliat  the 
line  PM"  is  tangent  to  the  surface  of  the  earth,  the  angle 
CM"  Pis  called  the  horizontal  parallax.  The  horizontal  paral- 
lax is  equal  to  the  angle  ivhich  the  radius  of  the  earth  subtends  as 
seen  from  the  object.  AVhen  we  say  that  the  horizontal  parallax 
of  the  moon  is  57',  and  that  of  the  sun  8".85,  it  is  the  same 
thing  as  saying  tliat  tlie  diameter  of  the  earth  subtends  twice 
those  angles  as  seen  from  the  moon  and  sun  respectively. 

Owing  to  tlie  ellipticity  of  the  earth,  all  its  diameters  will 
not  subtend  the  same  angle ;  the  polar  diameter  being  the 
shortest  of  all,  and  the  equatorial  the  loiigest.  The  equatorial 
diameter  is,  therefore,  adopted  by  astronomers  as  the  standard 
for  parallax.  The  coi-responding  parallax,  that  is,  the  equato- 
rial radius  of  the  earth  as  seen  from  a  celestial  body,  is  called 
the  Equatorial  Horizontal  Parallax  of  that  body. 


170  PRACTICAL  ASTBONOMT. 

To  measure  directly  the  distance  of  the  moon  or  any  other 
heavenly  body,  the  hne  PC  must  be  replaced  by  the  line  join- 
ing the  positions  of  the  two  observers,  called  the  base-line. 
Knowing  the  length  and  direction  of  this  base-line,  and  the 
difference  of  directions,  or  parallax,  the  distance  is  at  once  ob- 
tained. If  tlie  absolute  length  of  the  base-line  should  not  be 
known,  the  astronomer  could  still  determine  the  proportion 
of  the  distance  of  the  object  to  the  base-line,  leaving  the  tinal 
determination  of  the  absolute  distances  to  be  made  when  the 
base-line  could  be  measured. 

It  is  not  always  necessary  for  two  observers  actually  to  sta- 
tion themselves  in  two  distant  parts  of  the  earth  to  determine 
a  parallax.  If  the  observer  himself  could  move  along  the 
base-line,  and  keep  up  a  series  of  observations  on  the  object,  to 
see  how  it  seemed  to  move  in  the  opposite  direction,  he  would 
still  be  able  to  determine  its  distance.  Now,  every  observer  is 
actually  carried  along  by  two  such  motions,  because  he  is  on 
the  moving  earth.  He  is  carried  round  tlie  sun  every  year, 
and  round  the  axis  of  the  earth  every  day.  We  have  already 
shown  how,  in  consecpience  of  the  first  motion,  all  the  planets 
seem  to  describe  a  series  of  epicycles.  This  apparent  motion 
is  an  effect  of  parallax,  and  by  means  of  it  the  proportions  of 
the  solar  system  can  be  determined  Math  extreme  accuracy. 
The  base-line  is  the  diameter  of  the  earth's  orbit.  But  the 
parallax  in  question  does  not  help  us  to  determine  this  base- 
line. To  find  it,  we  must  first  know  the  distance  of  the  earth 
from  the  sun,  and  here  we  have  no  base-line  but  the  diameter 
of  the  earth  itself.  Nor  can  the  annual  motion  of  the  earth 
round  the  sun  enable  ns  to  determine  the  distance  of  the 
moon,  because  the  latter  is  carried  round  by  the  same  motion. 

The  result  of  the  daily  revolution  of  the  observer  round  the 
earth's  axis  is,  that  the  appai-ent  movement  of  the  planet  along 
its  course  is  not  perfectly  uniform  :  M'hen  the  observer  is  east, 
the  planet  is  a  little  to  the  west,  and  vice  versa.  By  observing 
the  small  inequalities  in  the  motion  of  the  planet  correspond- 
ing to  the  rotation  of  the  earth  on  its  axis,  we  have  the  means 
of  observinc:  its  distance  with  the  eartli's  diameter  as  a  base- 


PABALLAX  IN  GENERAL.  171 

line,  and  this  diameter  is  well  known.  Unfortunately,  how- 
ever, the  earth  is  so  small  compared  with  tlie  distances  of  the 
planets,  tliat  the  parallax  in  question  almost  eludes  measure- 
ment, except  in  the  case  of  those  planets  which  are  nearest 
the  earth,  and  even  then  it  is  so  minute  that  its  accurate  de- 
termination is  one  of  the  most  difficult  problems  of  modern 
astronomy. 

The  principal  difficulty  in  determining  a  parallax  from  the 
revolution  of  the  observer  around  the  earth's  axis  is  that  the 
observations  are  not  to  be  made  in  the  meridian,  but  when  the 
planet  is  near  the  horizon  in  the  east  and  west.  Hence  the 
most  accurate  and  convenient  instrument  of  all,  the  meridian 
circle,  cannot  be  used,  and  recourse  must  be  had  to  methods 
of  observation  subject  to  many  sources  of  error. 

In  measuring  very  minute  parallaxes,  it  may  be  doubtful 
whether  the  position  of  the  body  on  the  celestial  sphere  can 
be  determined  with  the  necessary  accuracy.  In  this  case  re- 
sort is  sometimes  had  to  relative  parallax.  By  this  is  meant 
the  difference  between  the  parallaxes  of  two  bodies  lying  near- 
ly in  the  same  direction.  The  most  notable  example  of  this 
is  afforded  by  a  transit  of  Venus  over  the  face  of  the  sun. 
To  determine  the  absolute  direction  of  Venus  when  nearest 
the  eartli  with  the  accuracy  required  in  measurements  of  par- 
allax has  not  hitherto  been  found  practicable,  because  the  ob- 
servation must  be  made  in  the  daytime,  when  the  atmosphere 
is  much  disturbed  by  the  rays  of  the  sun,  and  also  because 
only  a  small  part  of  the  planet  can  then  be  seen.  But  if  the 
planet  is  actually  between  us  and  the  sun,  so  as  to  be  seen  pro- 
jected on  the  sun's  face,  the  apparent  distance  of  the  planet 
from  the  centre  or  from  tlie  limb  of  the  sun  may  be  fouud 
with  considerable  accuracy.  Moreover,  this  distance  will  be 
different  as  seen  from  different  parts  of  the  earth's  surface  at 
the  same  moment,  owing  to  the  effect  of  parallax ;  that  is,  dif- 
ferent observers  will  see  Venus  projected  on  different  parts  of 
the  sun's  face.  But  the  change  thus  observed  will  be  only 
that  due  to  the  difference  of  the  parallaxes  of  the  two  bodies; 
while  both  change  their  directions,  that  nearest  the  observer 


172  PRACTICAL  ASTRONOMY. 

changes  the  more,  and  thus  seems  to  move  past  the  other,  ex- 
actly as  in  the  diagram  of  the  lights. 

It  may  be  asked  how  the  parallax  of  the  sun  can  be  found 
from  observations  of  the  transit  of  Venus,  if  such  observations 
show  only  the  difference  between  the  parallax  of  Venus  and 
that  of  the  sun.  We  reply  that  the  ratio  of  the  parallaxes  of 
the  two  bodies  is  known  with  great  precision  from  the  propor- 
tions of  the  system.  We  have  already  shown  that  these  pro- 
portions are  known  with  great  accuracy  from  the  third  law  of 
Kepler,  and  from  the  annual  parallax  produced  by  the  revolu- 
tion of  the  earth  round  the  sun.  It  is  thus  known  that  at  the 
time  of  the  transit  of  Venus,  in  1S74,  the  sun  was  nearly  four 
times  the  distance  of  Venus,  or,  more  exactly,  that  he  was 
3.783  times  as  far  as  that  planet.  Consequently,  the  parallax 
of  Venus  was  then  3.783  times  that  of  the  sun.  The  differ- 
ence of  the  parallaxes,  that  is,  the  relative  parallax,  must  then 
have  been  2.783  times  the  sun's  parallax.  Consequently,  we 
have  only  to  divide  the  relative  parallax  found  from  the  ob- 
servations by  2.783  to  have  the  parallax  of  the  sun  itself. 

Still  another  parallax,  seldom  applied  except  to  the  fixed 
stars,  is  the  Annual  Parallax.  This  is  the  parallax  already  ex- 
plained as  due  to  the  annual  revolution  of  the  earth  in  its  or- 
bit. It  is  equal  to  the  angle  subtended  by  the  line  joining  the 
earth  and  sun,  as  seen  from  the  star  or  other  body.  When  we 
say  that  the  annual  parallax  of  a  star  is  one  second  of  arc,  it  is 
the  same  thing  as  spying  that  at  the  star  tlie  line  joining  the 
earth  and  sun  would  subtend  an  apparent  angle  of  one  sec- 
ond, or  that  the  diameter  of  the  earth's  orbit  would  appear  un- 
der an  angle  of  two  seconds. 

It  will  be  seen  that  the  measurement  of  the  heavens  involves 
two  separate  operations.  The  one  consists  in  the  determina- 
tion of  the  distance  between  the  earth  and  the  sun,  wliich  is 
made  to  depend' on  the  solar  parallax,  or  the  angle  which  the 
semidiameter  ofrthe  earth  subtends  as  seen  from  the  sun,  and 
which  is  the  unit  of  distance  in  celestial  measurements.  The 
other  consists  in  the  determination  of  the  distances  of  the  stars 
and  planets  in  terms  of  this  unit,  which  gives  what  we  may 


MEASURES  OF  TEE  DISTANCE  OF  THE  SUN.  173 

call  the  proportions  of  the  universe.  Knowing  this  proportion, 
we  can  determine  all  the  distances  of  the  universe  when  the 
length  of  our  unit  or  the  distance  of  the  sun  is  known,  but  not 
before.  The  determination  of  this  distance  is,  therefore,  one 
of  the  capital  problems  of  astronomy,  as  well  as  one  of  the  most 
difficult,  to  the  solution  of  which  botli  ancient  and  modern  as- 
tronomers have  devoted  many  efforts. 

§  2.  Measures  of  the  Distance  of  the  Sun. 

We  have  already  shown,  in  describing  the  phases  of  the 
moon,  how  Aristarchus  attempted  to  determine  the  distance 
of  the  sun  by  measuring  the  angle  between  the  sun  and  the 
moon,  when  the  latter  appeared  half  illuminated.  From  this 
measure,  the  sun  was  supposed  to  be  twenty  times  as  far  as 
the  moon ;  a  result  which  arose  solely  from  the  accidental  er- 
rors of  the  observations. 

Another  method  of  attacking  the  problem  was  applied  by 
Ptolemy,  but  is  probably  due  to  Ilipparchus.  It  rests  on  a 
very  ingenious  geometrical  construction  founded  on  the  prin- 
ciple that  the  more  distant  the  sun,  the  narrower  will  be  the 
shadow  of  the  earth  at  the  distance  of  tlie  moon.  The  actual 
diameter  was  detennined  from  an  ingenious  combination  of 
two  partial  eclipses  of  the  moon,  in  one  of  which  half  of  the 
moon  was  south  of  the  limit  of  the  shadow,  Avhile  in  the  other 
three-fourths  of  her  diameter  was  north  of  the  limit;  that  is, 
one  fourth  of  the  moon's  disk  was  eclipsed.  It  was  thus  found 
that  tlie  moon's  apparent  diameter  was  31^',  and  the  appar- 
ent diameter  of  the  shadow  40f' .  The  former  innnber  was 
certainly  remarkably  near  the  truth.  From  tiiis  it  was  con- 
cluded that  the  sun's  parallax  was  3'  11",  and  his  distance  1210 
,radii  of  the  earth.  This  result  was  an  entire  mistake,  arising 
from  the  uncertainty  of  any  measure  of  so  small  an  angle. 
Keally,  the  parallax  is  so  minute  as  to  elude  all  measurement 
with  any  instrument  in  which  the  vision  is  not  assisted  by  the 
use  of  a  telescope.  Yet  this  result  continued  to  jBgure  in  as- 
tronomy through  the  fourteen  centuries  during  which  the"J?- 
magest''''  of  Ptolemy  was  the  supreme  authority,  without,  appar- 


174  PRACTICAL  ASTEOXOMY. 

ently,  any  astronomer  being  bold  enough  to  seriously  under- 
take its  revision. 

Kepler  and  his  contemporaries  saw  clearly  that  this  distance 
must  be  far  too  small ;  but  all  their  estimates  fell  short  of  the 
truth.  Wendell  came  nearest  the  truth,  as  he  claimed  that 
the  parallax  could  not  exceed  15".  But  the  best  estimate  of 
the  seventeenth  century  was  made  by  Huyghens,*  the  reason 
why  it  was  the  best  being  that  it  was  not  founded  on  any 
attempt  to  measure  the  parallax  itself,  which  was  then  real- 
ly incapable  of  measurement,  but  on  the  probable  magnitude 
of  the  earth  as  a  planet.  The  parallax  of  the  sun  is,  as  al- 
ready explained,  the  apparent  semidiameter  of  the  earth  as 
seen  from  the  sun.  If,  then,  we  can  find  what  size  the  earth 
would  appear  if  seen  from  the  sun,  the  problem  would  at  once 
be  solved.  The  apparent  magnitudes  of  the  planets,  as  seen 
from  the  earth,  are  found  by  direct  measurement  with  the 
telescope.  The  pi-oportions  of  the  solar  system  being  known, 
as  already  explained,  it  is  very  easy  to  determine  the  magni^ 
tudes  of  all  the  planets  as  seen  from  the  sun,  the  eartli  alone 
excepted.  The  idea  of  Iluyghens  was  that  the  earth,  being  a 
planet,  its  magnitude  would  probably  be  somewhere  near  that 
of  the  average  of  the  two  planets  on  each  side  of  it,  namely, 
Venus  and  Mai-s.  So,  taking  the  mean  of  the  diameters  of 
Venus  and  Mars,  and  supposing  this  to  represent  the  diameter 
of  the  earth,  he  found  the  angle  which  the  semidiameter  of 
the  supposed  earth  would  subtend  from  the  sun,  which  would 
be  the  solar  parallax. 

Although  this  method  may  look  like  a  happy  mode  of 
guessing,  it  was  much  more  reliable  than  any  which  had  be- 
fore been  applied,  for  the  reason  that,  in  supposing  the  mag- 
nitude of  the  earth  to  be  between  those  of  Venus  and  Mai*s, 
he  was  likely  to  be  nearer  the  truth  than  any  measure  of  ar» 
angle  entirely  invisible  to  the  naked  eye  would  be. 

An  nttempt  of  the  same  kind  made  by  Horrox,  celebrated 
in  the  history  of  astronomy  as  the  first  observer  of  a  transit 

*  At  the  close  of  liis  "Svstema  Satnmium." 


MEASURES  OF  THE  DISTANCE  OF  THE  SUX.  175 

of  Venus,  is  also  worthy  of  mention.  He  held  a  tlieorv,  which 
we  now  know  to  be  erroneous,  that  the  diameters  of  the  plan- 
ets were  proportional  to  their  distances  from  the  sun,  so  that 
their  angular  diameter  as  seen  from  the  sun  would  be  the 
same  for  them  all.  This  angular  diameter  ho  estimated  at 
28".  The  solar  parallax  being  equal  to  tlie  semi-diameter  of 
the  earth,  as  seen  from  the  sun,  it  would  follow  from  this  that 
the  solar  parallax  was  14".  Tin's  result,  though  much  farther 
from  the  truth  than  that  of  ITuj-ghens,  was  a  great  advance 
on  any  that  had  preceded  it. 

We  now  come  to  the  modern  methods  of  measuring  the 
paraUax  of  the  sun.  These  consist,  not  in  measuring  this  par- 
allax directly,  because  this  cannot  even  now  be  done  with  any 
accuracy,  but  in  measuring  the  parallax  of  one  of  the  planets 
Venus  and  Mars  when  nearest  the  earth.  These  planets  pass- 
ing from  time  to  time  much  nearer  to  us  than  the  sun  does, 
have  then  a  much  larger  parallax,  and  one  \vhich  can  easily 
be  measured.  Having  the  parallax  of  the  planet,  that  of  the 
sun  is  determined  from  the  known  proportion  between  their 
i-espective  distances. 

The  first  application  of  this  method  was  made  by  the  French 
astronomers  to  the  planet  Mars.  In  1671  they  sent  an  ex- 
pedition to  the  colony  of  Cayeime,  in  South  America,  Mhich 
made  observations  of  the  position  of  Mars  during  the  o})posi- 
tion  of  1672,  while  corresponding  observations  were  made  at 
the  Paris  Observator^^  The  difference  of  the  two  a])i\'uent 
positions,  reduced  to  the  same  moment,  gave  the  parallax  of 
Mars.  From  a  discussion  of  these  observations,  Cassini  con- 
cluded the  parallax  of  the  sun  to  be  9".5,  corresponding  to  a 
distance  of  the  sun  equal  to  21,600  semidiameters  of  the  cuith. 
This  distance  was  as  much  too  small  as  Huyghens's  w-as  too 
great,  so  that,  as  we  now  know,  no  real  improvement  was 
made.  Still,  the  data  were  much  more  certain  than  those  on 
which  the  estimate  of  Huyghens  was  made,  and  for  a  hundred 
years  it  was  generally  considered  that  the  sun's  parallax  was 
about  10",  and  his  distance  between  80  and  90  millions  of  miles. 

The  method  by  observations  of  Mars  is  still,  in  some  of  its 
I  13 


176  PRACTICAL  ASTRONOMY. 

forms,  among  tlie  most  valuable  which  have  been  applied  to 
the  determination  of  tlie  solar  parallax.  About  once  in  six- 
teen years  Mars  approaches  almost  as  near  the  earth  as  Venus 
does  at  the  times  of  her  transits,  the  favorable  times  being 
those  when  Mars  at  opposition  is  near  his  perihelion.  His 
distance  outside  the  earth's  orbit  is  tlien  only  0.373  of  the  as- 
tronomical unit,  or  34^^  millions  of  miles,  while  at  his  aphe- 
lion the  distance  is  nearly  twice  as  great.  At  the  nearest  op- 
positions, his  paralUix  is  over  23'',  an  angle  which  can  be  meas- 
ured with  some  accuracy.  The  displacement  of  the  planet 
due  to  parallax  is  then  found  by  comparing  the  results  of  ob- 
servations in  the  two  hemispheres. 

An  expedition  of  this  sort  was  that  of  Captain  James  M. 
GfUisSjlate  of  the  United  States  Navy,  who  went  out  to  Chili  in 
1849,  and  remained  till  1S52,  for  the  purpose  of  observing  the 
parallaxes  of  both  Venus  and  Mars.  The  most  recent  expe- 
dition was  that  made  to  the  Island  of  Ascension,  in  the  year 
1877,  by  Mr.  David  Gill,  now  Astronomer  Royal  at  the  Cape 
of  Good  Hope.  In  that  year  the  opposition  of  Mars  occurred 
within  a  few  days  of  the  time  of  his  passing  perihelion,  so  that 
he  approached  nearer  the  earth  than  at  any  time  witliin  the 
last  thirty  years.  Mr.  Gill  took  advantage  of  this  circum- 
stance to  determine  the  parallax  by  the  aid  of  the  heliometer. 
He  did  not,  however,  depend  upon  corresponding  observations 
in  other  regions  of  the  earth,  but  planned  out  his  work  so  as 
to  measure  the  change  in  the  direction  of  Mars  as  the  ob- 
server was  carried  around  by  the  rotation  of  the  earth.  In 
consequence  of  this,  when  Mars  was  near  either  horizon  he 
would  appear  lower  down  than  if  he  were  viewed  from  the 
centre  of  the  earth.  The  Island  of  Ascension  being  near  tlie 
equator,  the  direction  down  when  Mars  was  in  the  east  would 
be  nearly  opposite  the  corresponding  direction  when  Mars 
was  in  the  west.  Consequently,  the  motion  of  Mars  would 
not  be  perfectly  uniform  and  regular,  but  there  would  be  a 
daily  oscillation  due  to  parallax  which  Mr.  Gill  undertook  to 
measure.  The  final  result  of  his  observations  gave  8".78  for 
the  solar  parallax. 


&' 


SOLAE  PABALLAX  FROM  TRANSITS  OF  VENUS. 


177 


§  3,  Solar  Parallax  from  Transits  of  Venus. 

The  most  celebrated  method  of  determining  the  solar  paral- 
lax has  been  by  transits  of  Venus  over  the  face  of  the  sun,  by 
which  the  difference  between  the  parallax  of  the  planet  and 
that  of  the  sun  can  be  found,  as  explained  in  §  1.  We  know 
from  our  astronomical  tables  that  this  phenomenon  has  recur- 
red in  a  certain  regular  cycle  four  times  every  243  years  for 
many  centuries  past.  This  cycle  is  made  up  of  four  intervals, 
the  lengtlis  of  which  are,  in  regular  order,  105|^  years,  8  years, 
121^  years,  8  years,  after  which  the  intervals  repeat  them- 
selves. The  dates  of  occurrence  for  eight  centuries  are  as 
follows : 


1518 June  2(1. 

152G June  1st. 

1631 December  7th. 

1639 December  4th. 

1761 June  5th. 

1769 June  3d. 

1874 December  9th. 


1882 December  Gth. 

2004 June  8th. 

2012 June  6th. 

2117 December  11th. 

2125 December  8th. 

2247 June  Uth. 

2255 June  9th. 


It  has  been  only  in  comparatively  recent  times  that  this  phe- 
nomenon could  be  predicted  and  observed.  In  the  years  1518 
and  1526  the  idea  of  looking  for  such  a  thing  does  not  seem 
to  have  occurred  to  any  one.  The  following  century  gave 
birth  to  Kepler,  who  so  far  improved  the  planetary  tables 
as  to  predict  that  a  transit  would  occur  on  December  Gth, 
1631.  But  it  did  not  commence  until  after  sunset  in  Eu- 
rope, and  was  over  before  sunrise  next  morning,  so  that  it 
passed  entirely  unobserved.  Unfortunately,  the  tables  were 
so  far  from  accurate  that  they  failed  to  indicate  the  transit 
which  occurred  eight  years  later,  and  led  Kepler  to  announce 
that  the  phenomenon  would  not  recur  till  1761.  The  transit 
of  1639  w^ould,  therefore,  like  all  former  ones,  have  passed 
entirely  unobserved,  had  it  not  been  for  the  talent  and  enthu- 
siasm of  a  young  Englishman.  Jeremiah  Ilorrox  M-as  then  a 
young  curate  of  eighteen,  residing  in  the  North  of  England, 
who,  even  at  that  early  age,  was  a  master  of  the  astronomy  of 


ITS  PRACTICAL  ASTEOXOMY. 

his  times.  Compariug  different  tables  with  his  own  observa- 
tions of  Yenus,  he  found  that  a  transit  might  be  expected  to 
occur  on  December  4th,  and  prepared  to  observe  it,  after  the 
fashion  then  in  vogue,  by  letting  the  image  of  the  sun  passing 
through  his  telescope  fall  on  a  screen  behind  it.  Unfortu- 
nately, the  day  was  Sunday,  and  his  clerical  duties  prevented 
his  seeing  the  ingress  of  the  planet  upon  the  solar  disk — a  cir- 
cumstance which  science  has  mourned  for  a  century  past,  and 
will  have  reason  to  mourn  for  a  centnry  to  come.  "When  he 
returned  from  church,  he  was  overjoyed  to  see  the  planet  upon 
the  face  of  the  sun,  but,  after  following  it  half  an  hour,  the  ap- 
proach of  sunset  compelled  him  to  suspend  liis  observations. 

During  the  interval  between  this  and  tlie  next  transit,  which 
occurred  in  1761,  exact  astronomy  made  very  rapid  progress, 
through  the  discovery  of  the  law  of  gravitation  and  the  ap- 
plication of  the  telescope  to  celestial  measurements.  A  great 
additional  interest  was  lent  to  the  phenomenon  by  Halley's 
discovery  that  observations  of  it  made  from  distant  points  of 
the  earth  could  be  used  to  determine  the  distance  of  the  sun. 

The  principles  by  which  the  parallaxes,  and  therefore  the 
distances,  of  Yenus  and  the  sun  are  determined  by  Halley's 
method  are  quite  simple.  In  consequence  of  the  parallax  of 
Yenus,  two  observers  at  distant  points  of  the  earth's  surface, 

watching  her  course  over  the 
solar  disk,  will  see  her  describe 
slightly  different  paths,  as  shown 
in  Fig.  50.  It  is  by  the  distance 
between  these  paths  that  the  par- 
allax has  hitherto  been  deter- 
mined. 

The  essential  principle  of  Hal- 
ley's  method  consists  in  the  mode 
fio.to.-Apparent  paths  of  Venus  across  of  determining  the  distance  be- 

the  suD,  as  seen  from  diflferent  stations  tweeu  these  apparent  13aths.      All 

during  the  transit  of  1S74.    The  upper  .  .  r    i      ^  mi    i_ 

path  is  that  seen  from  a  Honthera  sta-  mspCCtlOU  ot  the  hgure  Will  shoW 

tion :   the  lower  is  that  seen  froni  a  ^i^^^    ^j^g       ^^j^   farthest   from    tllC 
northern  station,  bnt  the  distance  be-  '■ 

t ween  the  paths  is  exaggerated.  sun's  Centre  is  shorter  than  the 


SOLAB  PARALLAX  FROM  TRANSITS  OF  VENUS.         179 

other,  so  that  Venus  will  pass  over  the  sun  more  quickly  when 
watched  from  a  southern  station  than  when  watched  from  a 
northern  one.  llalley  therefore  proposed  that  the  different  ob- 
servers should,  with  a  telescope  and  a  chronometer,  note  the 
time  it  took  Venus  to  pass  over  the  disk,  and  the  difference  be- 
tween these  times,  as  seen  from  different  stations,  would  give 
the  means  of  determining  the  difference  between  the  parallaxes 
of  Venus  and  the  sun.  The  ratio  between  the  distances  of 
the  planet  and  the  sun  is  known  with  great  exactness  by  Kep- 
ler's third  law,  from  which,  knowing  the  differences  of  paral- 
laxes, the  distance  of  each  l)ody  can  be  determined. 

By  this  plan  of  Halley  the  observer  must  note  with  great 
exactness  the  times  both  of  beginning  and  end  of  the  transit. 
There  are  two  phases  whicli  may  be  observed  at  the  beginning 
and  two  at  the  end,  making  four  in  all, 

TJie  first  is  that  when  the  planet  first  touches  the  edge  of 
the  solar  disk,  and  begins  to  make  a  notch  in  it,  as  at  a,  Fig.  50. 
This  is  q,^\\q&  first  external  contact. 

The  second  is  that  when  the  planet  has  just  entered  entirely 
upon  the  sun,  as  at  h.     This  is  (iaWadi  first  internal  contact. 

The  third  contact  is  that  in  which  the  planet,  after  crossing 
the  sun,  first  reaches  the  edge  of  the  disk,  and  begins  to  go 
off,  as  at  c.     This  is  called  second  internal  contact. 

The  fourth  contact  is  that  in  which  the  planet  finall}'  disap- 
pears from  the  face  of  the  sun,  as  at  d.  This  is  called  second 
external  contact. 

Kow,  it  was  tlie  opinion  of  Halley,  and  a  very  plausible  one, 
too,  that  the  internal  contacts  could  be  observed  with  far  gi-eat- 
er  accuracy  than  the  external  ones.  He  founded  this  opinion 
on  his  own  experience  in  observing  a  transit  of  the  planet  Mer- 
cury at  St,  Helena  in  1G77,  It  will  be  seen  by  inspecting  Fig. 
51,  which  represents  the  position  of  the  planet  just  before  first 
internal  contact,  that  as  the  planet  moves  forward  on  the  solar 
disk  the  shar])  horns  of  light  on  each  side  of  it  approach  each 
other,  and  tliat  the  moment  of  internal  contact  is  marked  by 
these  horns  meeting  each  other,  and  forming  a  thread  of  light 
all  the  way  across  the  dark  space,  as  in  Fig,  52.     This  thread 


180 


PEA  CTIGAL  ASTE  OXOMY. 


of  light  is  indeed  simply  the  extreme  edge  of  the  sun's  disk 
coming  into  view  behind  the  planet.  In  observing  the  tran- 
sit of  Mercury,  Halley  felt 
sure  that  he  could  fix  the 
moment  at  which  the  horns 
met,  and  the  edge  of  the 
sun's  disk  appeared  un- 
broken, within  a  single  sec- 
ond; and  he  hence  con- 
cluded that  observei-s  of 
the  transit  of  Yenus  could 
observe  the  time  required 

Fig.  51.— Venus  approaching  internal  contact  on  101'  V  CnUS  tO  paSS  acrOSS 
the  face  of  the  snu.  The  planet  is  supposed  ^[^q  g^^^^  within  One  Or  tWO 
to  be  moving  upward.  i       mi 

seconds.  1  hese  times  would 
differ  in  different  parts  of  the  earth  by  fifteen  or  twenty  min- 
utes, in  consequence  of  parallax.  Hence  it  followed,  that  if 
Halley's  estimate  of  the  de- 
gree  of  accuracy  attainable 
were  correct,  the  parallax  of 
Venus  and  the  sun  would  be 
determined  by  the  proposed 
system  of  observations  within 
the  six  hundredth  of  its  whole 
amount. 

When  the  long-expected  5th 
of  June,  1761,  at  length  ap- 
proached, which  was  a  gener- 
ation after  Halley's  death,  ex- 
peditions were  sent  to  distant 
parts  of  the  world  by  the  principal  European  nations  to  make 
the  required  observations.  The  French  sent  out  from  among 
their  astronomers,  Le  Gentil  to  Pond  i cherry ;  Pingre  to  Rod- 
riguez Island,  in  the  neighborhood  of  the  Mauritius ;  and  the 
Abbe  Chappe  to  Tobolsk,  in  Siberia.  The  war  with  England, 
unfortunately,  prevented  the  first  two  from  reaching  their  sta- 
tions in  time,  but  Chappe  was  successful.    From  England,  Ma- 


FiG.  62.— Internal  contact  of  the  limb  of  Ve- 
nns  with  that  of  the  sun. 


SOLAR  PARALLAX  FROM  TRANSITS  OF  VENUS. 


181 


son — lie  of  tlie  celebrated  Mason  and  Dixon's  Line — was  sent 
to  Sumatra;  but  he,  too,  was  stopped  by  the  war:  Maskelyne, 
the  Astronomer  Royal,  was  sent  to  St.  Helena.  Denmark, 
Sweden,  and  Russia  also  sent  out  expeditions  to  various  points 
in  Europe  and  Asia. 

With  those  observers  who  were  favored  by  fine  weathei",  the 
entry  of  the  dark  body  of  Yenus  upon  the  limb  of  the  sun 
was  seen  very  well  until  the  critical  moment  of  internal  con- 
tact approached.  Then  they  were  perplexed  to  Und  tliat  the 
planet,  instead  of  preserving  its  circular  form,  appeared  to 
assume  the  shape  of  a  pear  or  a  balloon,  the  elongated  portion 
being  connected  with  tlie  limb  of  the  sun.  We  give  two  fig- 
ures, 52  and  53,  the  first  showing  how  the  planet  ought  to  have 
looked,  the  last  how  it  really  did  look.  Now,  we  can  readily 
see  that  the  observer,  looking 
at  such  an  appearance  as  in 
Fig.  53,  M'ould  be  nnable  to 
say  whether  internal  contact 
had  or  had  not  taken  place. 
The  round  jmrt  of  the  planet 
is  entirely  within  the  sun,  so 
that  if  he  judged  from  this 
alone,  he  would  say  that  in- 
ternal contact  is  passed.  But 
the  horns  are  still  separated 
by  this  dai'k  elongation,  or 
"black  drop,"  as  it  is  general- 
ly called,  so  that,  judging  from  this,  internal  contact  has  not 
taken  place.  The  result  was  an  uncertainty  sometimes  amount- 
ing to  nearly  a  minute  in  observations  which  were  expected  to 
be  correct  within  a  single  second. 

When  the  parties  returned  home,  and  their  observations 
were  computed  by  various  astronomers,  the  resulting  values 
of  the  solar  parallax  were  found  to  range  from  S".5,  found  by 
Short  of  England,  to  10",5,  found  by  Pingrc,  of  Fraiice,  so 
that  there  was  nearly  as  much  uncertainty  as  ever  in  the  value 
of  the  element  sought.     Nothing  daunted,  however,  prepara- 


FiG.  53.— The  black  drop,  or  ligarneut. 


182  PEACTICAL  ASTRONOMY. 

tions  yet  more  extensive  were  made  to  observe  the  transit  of 
1769.  Among  the  observers  was  one  whose  patience  and 
whose  fortune  must  excite  our  warmest  sympatliies.  "We  have 
said  that  Le  Gentil,  sent  out  by  the  French  Academy  to  ob- 
serve the  transit  of  1761  in  the  East  Indies,  was  prevented 
from  reaching  liis  station  by  the  war  with  England.  Finding 
the  lirst  port  he  attempted  to  reach  in  the  possession  of  the 
English,  his  commander  attempted  to  make  another,  and, 
meeting  witli  unfavorable  winds,  was  still  at  sea  on  the  day  of 
the  transit.  He  thereupon  formed  the  resolution  of  remain- 
ing, with  his  instrument?,  to  observe  the  transit  of  1769.  He 
was  enabled  to  support  himself  by  some  successful  mercantile 
adventures,  and  he  also  industriously  devoted  himself  to  scien- 
tific observations  and  inquiries.  The  long-looked-for  morning 
of  June  4th,  1769,  found  him  thoroughly  prepared  to  make 
the  observations  for  M-hich  he  had  waited  eight  long  years. 
The  sun  shone  out  in  a  cloudless  sky,  as  it  had  shone  for  a 
number  of  days  previously.  But  just  as  it  was  time  for  the 
transit  to  begin,  a  sudden  storm  arose,  and  the  sky  became 
covered  with  clouds.  "When  they  cleared  away  the  transit 
was  over.  It  was  two  weeks  before  the  ill-fated  astronomer 
could  hold  the  pen  which  was  to  tell  his  friends  in  Paris  the 
story  of  his  disappointment. 

In  this  transit  the  ingress  of  Venns  on  the  limb  of  the  sun 
occurred  just  before  the  sun  was  setting  in  Western  Europe, 
which  allowed,  numbers  of  observations  of  the  first  two  phases 
to  be  made  in  England  and  France.  The  commencement  was 
also  visible  in  this  country — which  was  then  these  colonies — 
under  very  favorable  circumstances,  and  it  was  well  observed 
by  the  few  astronomers  we  then  had.  The  leader  among 
these  was  the  talented  and  enthusiastic  Rittenliouse,  who  was 
already  well  known  for  his  industry  as  an  observer.  The  ob- 
servations were  organized  under  the  auspices  of  the  American 
Philosophical  Society,  then  in  the  vigor  of  its  youth,  and  par- 
ties of  observei-s  were  stationed  at  Norristown,  Philadelphia, 
and  Cape  Henlopen.  These  observations  have  every  appeai*- 
ance  of  being  among  the  most  accurate  made  on  the  transit; 


SOLAR  PARALLAX  FROM  TRANSITS  OF  VENUS.         183 

but  they  have  not  received  the  consideration  to  which  they  are 
entitled,  partly,  we  suppose,  because  the  altitude  of  the  sun 
was  too  great  to  admit  of  their  being  of  much  value  for  the 
determination  of  parallax,  aud  partly  because  they  were  not 
yery  accordant  with  the  European  observations. 

The  phenomena  of  the  distortion  of  the  planet  and  the 
"black  drop,"  already  described,  were  noticed  in  this,  as  in 
the  preceding  transit.  It  is  strongly  indicative  of  tlie  ill 
preparation  of  the  observers  that  it  seems  to  have  taken  them 
all  by  surprise,  except  the  few  who  had  observed  the  preced- 
ing transit.  The  cause  of  the  appearance  was  first  pointed 
out  by  Lalande,  and  is  briefly  this :  when  we  look  at  a  bright 
object  on  a  dark  ground,  it  looks  a  little  larger  than  it  real- 
ly is,  owing  to  the  encroachment  of  the  light  upon  the  dark 
border.  This  encroachment,  or  ii-radiation,  may  arise  from  a 
number  of  causes — imperfections  of  the  eye,  imperfections  of 
the  lenses  of  the  telescope  when  an  instrument  is  used,  and 
the  softening  effect  of  the  atmosphere  when  we  look  at  a  ce- 
lestial object  near  the  horizon.  To  understand  its  effect,  we 
ha^■e  only  to  imagine  a  false  edge  ])aintcd  in  white  around  the 
borders  of  the  bright  object,  the  edge  becoming  narrower  and 
darker  where  the  bright  object  is  reduced  to  a  very  narrow 
line.  Thus,  by  painting  around  the  borders  of  the  light  por- 
tions of  Fig.  51,  we  have  formed  Fig.  53,  and  produced  an  ap- 
pearance quite  similar  to  that  described  b}"^  the  observei*s  of 
the  ti'ansit.  The  better  the  telescope  and  the  steadier  the  at- 
mosphere, the  narrower  this  border  will  be,  and  the  more  the 
planet  will  seem  to  preserve  its  true  form,  as  in  Fig.  52.  In 
the  observations  of  the  recent  transit  of  Venus  with  the  im- 
proved instruments  of  the  present  time,  very  few  of  the  more 
fSxperienced  observers  noticed  any  distortion  at  all. 

The  results  of  the  observations  of  1769  were  much  more 
accordant  than  those  of  1761,  and  seemed  to  indicate  a  paral- 
lax of  about  8".5,  Curious  as  it  may  seem,  more  than  half  a 
century  elapsed  after  the  transit  before  its  results  were  com- 
pletely worked  up  from  all  the  observations  in  an  entirely 
satisfactory  manner.     This  was  at  length  done  by  Encke,  in 


1S4  PRACTICAL  ASTRONOMY. 

1824,  for  both  transits,  the  result  giving  S'^STTG  for  the  solar 
parallax.  Some  suspicion,  however,  attached  to  some  of  the 
observations,  which  he  was  not  at  that  time  able  to  remove. 
In  1835,  having  examined  the  original  records  of  the  observa- 
tions in  question,  he  corrected  his  work,  and  found  the  follow- 
ing separate  results  from  the  two  transits : 

Parallax  from  the  obsei-vations  of  17G1 ^ 8". 53 

Parallax  from  the  observ.itions  of  17G9 8". 59 

Most  probable  result  from  both  transits 8".571 

The  probable  error  of  the  result  was  estimated  at  0".037, 
which,  though  larger  than  was  expected,  was  much  less  than 
the  actual  eri-or  has  since  proved  to  be.  The  corresponding 
distance  of  the  sun  is  95,370,000  miles,  a  classic  number 
adopted  by  astronomers  everywhere,  and  familiar  to  every 
one  who  has  read  any  work  on  astronomy. 

This  result  of  Encke  was  received  without  question  for 
more  than  thirty  yeai-s.  Bnt  in  1854  the  celebrated  Hansen, 
completing  his  investigations  of  the  motions  of  the  moon, 
found  that  her  observed  positions  near  her  first  and  last  quar- 
ters could  not  be  accounted  for  except  by  supposing  the  par- 
allax of  the  sun  increased,  and  therefore  his  distance  dimin- 
ished, by  about  a  thirtieth  of  its  entire  amount.  The  exist- 
ence of  this  error  has  since  been  amply  confirmed  in  several 
wavs.  The  fact  is,  that  although  a  century  ago  a  transit  of 
Venus  afiorded  the  most  accurate  way  of  obtaining  the  dis- 
tance of  the  sun,  yet  the  great  advances  made  during  the 
present  generation  in  the  art  of  oliserving,  and  the  applica- 
tion of  scientific  methods,  have  led  to  other  means  of  greater 
accuracy  than  these  old  observations.  It  is  remarkable  that 
while  nearly  every  class  of  observations  is  now  made  with 
a  precision  which  the  astronomers  of  a  century  ago  never 
thought  possible,  yet  this  particular  observation  of  the  interior 
contact  of  a  planet  M'ith  the  limb  of  the  sun  has  never  beeji 
made  with  any  thing  like  the  accuracy  which  Ilalley  himself 
thought  he  attained  in  his  observation  of  the  transit  of  Mer- 
curv  two  centuries  ago. 


SOLAB  PARALLAX  FROM  TRANSITS  OF  VENUS.        185 

The  knowledge  of  this  error  in  the  fundamental  astronom- 
ical imit  gave  increased  interest  to  the  transit  of  Venus  which 
was  to  occur  on  December  8th,  1874.  The  rarity  of  the  phe- 
nomenon was  an  advantage,  in  that  it  led  to  an  amount  of 
public  interest  being  taken  in  it  which  could  not  have  been 
excited  by  any  otlier  astronomical  event,  and  thus  secured 
from  various  governments  the  grants  necessary  to  fit  out  the 
necessary  parties  of  observation.  Flans  of  observation  began 
to  be  worked  out  very  far  in  advance.  In  1857,  Professor 
Airy  sketched  a  general  plan  of  operations  for  the  observation 
of  the  transits,  and  indicated  the  regions  of  the  globe  in  which 
he  considered  the  observations  should  be  made.  In  1870,  be- 
fore any  steps  whatO^ver  were  taken  in  this  country,  he  had  ad- 
vanced so  far  in  his  preparations  as  to  have  his  observing  huts 
all  ready,  and  liis  instruments  in  process  of  construction.  In 
1869,  the  Prussian  Government  appointed  a  connnission,  con- 
sisting of  six  or  eight  of  its  most  eminent  astronomers,  to  de- 
vise a  plan  of  operations,  and  report  it  to  the  Government 
with  an  estimate  of  the  expenses.  About  the  same  time  tlie 
Russian  Government  began  making  extensive  preparations 
for  observing  the  transit  from  a  great  number  of  stations  in 
Siberia, 

Active  preparations  for  the  observations  in  question  were 
commenced  by  the  United  States  Government  in  1871.  An 
account  of  the  method  of  observation  adopted  by  the  Com- 
mission to  whom  the  matter  was  intrusted  may  not  be  devoid 
of  interest.  The  observations  of  the  older  transits  having 
failed  in  giving  results  of  the  accui-acy  now  required,  it  be- 
came necessary  to  improve  upon  the  system  then  adopted. 
In  this  system,  the  parallax  depended  entirely  on  observations 
of  contacts,  the  uncertainty  of  which  we  have  already  sliown, 
Besides  this  uncertainty,  Halley's  method  was  open  to  the  ob- 
jection that,  unless  both  contacts  were  observed  at  each  sta- 
tion, the  path  of  Venus  could  not  be  determined,  and  no  re- 
sult could  be  deduced.  It  was  therefore  proposed  by  De 
I'Isle  early  in  the  last  century,  that  the  observers  should  de- 
termine the  longitudes   of  their  stations,  in   order  that,  by 


186  PRACTICAL  ASTRONOMY. 

means  of  it,  they  could  find  the  actual  intervals  between  the 
moments  at  which  any  given  contact  was  seen  at  the  different 
stations.  This  method  was  an  improvement  on  Halley's,  in 
ihat  it  diminished  the  chances  of  total  failnre.  Still,  it  de- 
pended entirely  npon  making  an  accurate  observation  of  the 
moment  of  contact,  and  was  liable  to  fail  from  any  accident 
which  might  interfere  with  such  an  observation  —  a  passing 
cloud,  or  a  disarrangement  of  some  of  the  instruments  of  ob- 
servation. Besides,  it  was  not  yet  certain  whether  the  obser- 
vations could  be  made  with  the  necessary  accuracy.  It  was, 
therefore,  desirable  that,  instead  of  depending  on  contacts 
alone,  some  method  should  be  adopted  of  finding  the  position 
of  Venus  on  the  face  of  the  sun  as  often  as  possible  during 
the  four  houi-s  which  she  should  occupy  in  passing.  The 
easiest  and  most  effective  way  of  doing  this  seemed  to  be  to 
take  photographs  of  the  sun  with  Venus  on  his  disk,  which 
photographs  could  be  brought  home,  compared,  and  measured 
at  leisure. 

This  mode  of  astronomical  measurement  has  been  brought 
to  great  perfection  in  this  country  by  Mr.  L.  M.  Rutherfurd 
and  others,  and  has  been  found  to  give  results  exceeding  in 
accuracy  any  yet  attained  by  ordinary  eye  observations.  The 
advantages  of  the  photographic  method  are  so  obvious  that 
there  could  be  no  hesitation  about  employing  it,  and,  so  far 
as  is  known,  it  was  applied  by  every  European  nation  which 
sent  out  parties  of  observation.  But  there  is  a  great  and 
essential  difference  between  the  methods  of  photographing 
adopted  by  the  Americans  and  by  most  of  the  Europeans. 
The  latter  seem  to  have  devoted  all  their  attention  to  the 
problem  of  securing  a  good  sharp  photograpli,  taking  it  for 
granted  that  when  this  photograph  was  measured  there  would 
be  no  further  difificulty.  But  the  measurement  at  home  is 
necessarily  made  in  inches  and  fractions,  while  the  distance 
we  must  know  is  to  be  found  in  minutes  and  seconds  of  an- 
gular measure.  If  we  have  a  map  by  measurements  on  which 
we  desire  to  know  the  exact  distance  of  two  places,  we  must 
first  know  the  exact  scale  on  wliich  the  map  is  laid  down. 


SOLJB  PARALLAX  FROM  TRANSITS  OF  VENUS.         187 

with  a  degree  of  accuracy  corresponding  to  that  of  onr  meas- 
ures. Just  so  with  our  photographs  taken  at  various  parts  of 
the  globe.  We  must  know  the  scale  on  which  the  images  are 
photographed  before  we  can  derive  any  conclusions  from  our 
measures.  While  the  determination  of  this  scale  with  suffi- 
cient precision  for  ordinary  purposes  is  quite  easy,  this  is  by 
no  means  the  case  with  a  pi'oblem  where  so  much  accuracy 
was  required,  so  that  here  lay  the  greatest  difficulty  which  the 
photographic  method  offered. 

In  the  mode  of  photographing  adopted  by  the  Americans 
this  difficulty  was  met  by  using  a  telescope  of  great  length 
— nearly  forty  feet.  So  long  a  telescope  would  be  too  un- 
wieldy to  point  at  the  sun ;  it  was  therefore  fixed  in  a  hor- 
izontal position,  the  rays  of  the  sun  being  thrown  into  it  by  a 
mirror.  The  scale  of  the  pictui-e  was  determined  by  actually 
measuring  the  distance  between  the  object-glass  and  the  pho- 
tograph-plate. Each  station  was  supplied  with  special  appa- 
ratus by  which  this  measurement  could  be  made  within  the 
hundredth  of  an  inch.  Then,  knowing  the  position  of  the  op- 
tical centre  of  the  glass,  it  is  easy  to  calculate  exactly  liow 
many  inches  any  given  angle  will  subtend  on  the  photograph- 
plate.  The  following  brief  description  of  the  apparatus  will 
be  readily  understood  by  reference  to  the  figures : 

The  object-glass  and  the  support  for  the  mirror  are  mount- 
ed on  an  iron  pier  extending  four  feet  into  the  ground,  and 
firmly  embedded  in  concrete.  The  mirror  is  in  a  frame  at 
the  end  of  an  inclined  cast-iron  axis,  which  is  turned  with  a 
very  slow  motion  by  a  simple  and  ingenious  piece  of  clock- 
work. The  inclination  of  the  axis  and  the  rate  of  motion  are 
so  adjusted  that,  notwithstanding  the  diurnal  motion  of  the 
sun  —  or,  to  speak  more  accurately,  of  the  earth  —  the  sun's 
rays  will  always  be  reflected  in  the  same  direction.  This  re- 
sult is  not  attained  with  entire  exactness,  but  it  is  so  near  that 
it  will  only  be  necessary  for  an  assistant  to  touch  the  screws 
of  the  mirror  at  intervals  of  fifteen  or  twenty  minutes  during 
the  critical  hours  of  the  transit.  The  reflector  is  simply  a 
piece  of  finely  polished  glass,  without  any  silvering  whatever. 


188 


PRACTICAL  ASTSOXOMY. 


It  only  reflects  about  a  twentieth  of  the  sun's  light ;  but  so  in- 
tense are  his  rays  that  a  photograph  can  be  taken  in  less  than 
the  tenth  of  a  second.  The  polishing  of  this  mirror  was  the 
most  delicate  and  diflicult  operation  in  the  construction  of 
the  apparatus,  as  the  slightest  deviation  from  perfect  flatness 
would  be  fatal.  For  instance,  if  a  straight  edge  laid  upon  the 
glass  should  touch  at  the  edges,  but  be  the  hundred- thou- 
sandth of  an  inch  above  it  at  the  centre,  the  reflector  would 
be  useless.  It  might  have  seemed  hopeless  to  seek  for  such  a 
degree  of  accuracy,  had  it  not  been  for  the  confidence  of  the 
Commission  in  the  mechanical  genius  of  Alvan  Clark  &  Sons, 
to  whom  the  manufacture  of  the  apparatus  was  intrusted. 
The  mirrors  were  tested  by  observing  objects  through  a  tele- 
scope, first  directly,  and  then  by  reflection  from  the  mirror. 
If  they  were  seen  with  equally  good  definition  in  the  two 
cases,  it  would  show  that  there  were  no  irregularities  in  the 
surface  of  the  mirror;  while  if  it  were  either  concave  or  eon- 
vex,  the  focus  of  the  telescope  would  seem  shortened  or 
The  fii'st  test  was  sustained  perfectly,  while  the 


lengthened. 


\  'r 


\v 


OBTWICE  <:     s„tR,^, 

S9T  AMD  A  ma-joL      ^   ' 


Fio.  54 — Method  of  photogrnphing  the  transit  of  Venns  used  by  tlie  French  and  Ainerl« 
can  observers,  and  by  Lord  Lindsay. 


SOLAR  PARALLAX  FROM  TRANSITS  OF  VENUS.         189 

circles  of  convexity  or  concavity  indicated  by  the  changes  of 
focus  of  the  photographic  telescope  were  many  miles  in  di- 
ameter. 

Immediately  in  front  of  the  mirror  is  the  object-glass.  The 
curves  of  the  lenses  of  which  it  is  formed  are  so  arranged  that 
it  is  not  perfectly  achromatic  for  the  visual  rays,  but  gives  the 
best  photographic  image.  Thirty -eight  feet  and  a  fraction 
from  the  glass  is  the  focus,  where  an  image  of  the  sun  about 
four  and  a  quarter  inches  in  diameter  is  formed.  Here  an- 
other iron  pier  is  firmly  embedded  in  the  ground  for  the  sup- 
port of  the  photographic  plate -holder.  This  consists  of  a 
brass  frame  seven  inches  sqr.are  on  the  inside,  revolving  on  a 
vertical  rod,  which  passes  through  the  iron  plate  on  top  of  the 
pier.  Into  this  frame  is  cemented  a  square  of  plate-glass,  just 
as  a  pane  of  glass  is  puttied  in  a  window.  The  glass  is  divided 
into  small  squares  by  very  fine  lines  about  one-five-hundredth 
of  an  inch  thick,  which  were  etched  by  a  process  invented  and 
perfected  by  Mr.  W.  A.  Rogers,  of  the  Cambridge  Observatory. 
The  sensitive  plate  goes  into  the  other  side  of  the  frame,  and 
when  in  position  for  taking  the  photograph,  there  is  a  space 
of  about  one-eighth  of  an  inch  between  the  ruled  lines  and 
the  plate.  The  former  are,  therefore,  photographed  on  every 
picture  of  the  sun  which  is  taken,  and  serve  to  detect  any 
contraction  of  the  collodion  film  on  the  glass  plate. 

The  rod  on  which  the  plate-holder  turns,  and  the  frame  it- 
self, are  perforated  from  top  to  bottom  by  a  vertical  opening 
one-sixth  of  an  inch  in  diameter.  Through  the  centre  of  this 
opening,  passing  between  the  ruled  plate  and  the  photograph 
plate,  hangs  a  plumb-line  of  very  fine  silver  wire.  In  every 
picture  of  the  snn  this  plumb-line  is  also  photographed,  and 
this  marks  a  truly  vertical  line  on  the  plate  very  near  the  mid- 
dle vertical  etched  line.  A  spirit-level  is  fixed  to  the  top  of 
the  frame,  and  serves  to  detect  any  changes  in  the  inclination 
of  the  ruled  lines  to  the  horizon. 

One  of  the  most  essential  features  of  the  arrangement  is 
that  the  photographic  object-glass  and  plate-holder  are  on  the 
same  level,  and  in  the  meridian  of  the  transit  instrument  with 


190  PRACTICAL    ASTliOXOMY. 

which  tlie  time  is  determined.  The  central  ruled  line  on  the 
plate-holder  is  thus  used  as  a  meridian  mark  for  the  transit. 
The  great  advantage  of  this  arrangement  is,  that  it  permits 
the  angle  which  the  line  joining  the  centres  of  the  sun  and 
Venus  makes  with  the  meridian  to  be  determined  witii  the 
greatest  precision  by  means  of  the  image  of  the  plumb-line 
M'hich  is  photographed  across  the  picture  of  the  sun. 

If  this  method  of  photographing  were  applicable  only  to 
transits  of  Venus,  it  would  now  have  little  interest  for  the 
general  reader,  because  such  a  transit  will  not  again  occur 
until  the  year  2004;  but  the  instrument  can  be  applied  in 
any  case  where  a  photograph  of  the  sun  is  required.  It  can- 
not be  readily  applied  to  the  moon  or  stars,  because  a  longer 
exposure  is  then  necessary,  and  there  would  be  a  rotation  of 
the  image  around  the  centre  of  the  plate  whicii  would  inter- 
fere with  its  accuracy.  The  instrument  will  no  doubt  be  of 
use  in  accurately  photographing  eclipses  of  the  sun. 

The  work  of  reducing  the  observations  of  a  transit  of  Vonus, 
with  all  the  precision  required  by  modern  astronomy,  is  one 
involving  an  immense  mass  of  calculations  and  much  tedious 
investigation.  Before  the  final  result  can  be  attained,  it  is 
necessary  that  all  the  observations  made  under  the  auspices  of 
the  several  governments  which  took  part  in  the  work  shall  be 
reduced  and  published,  and,  after  this  is  done,  that  some  one 
shall  combine  them  all,  so  as  to  obtain  the  most  probable  re- 
sult. Partial  results,  founded  upon  a  portion  of  the  observa- 
tions, may,  indeed,  be  deduced  without  waiting  for  all  the 
material;  but  tlie  majority  of  the  leading  astronomers  con- 
ceive that  these  results  will  not  liave  any  scientific  interest; 
and  at  a  meeting  of  the  International  Astronomical  Society 
(the  Astronomische  Gesellschaft)^  held  at  Leyden,  it  was  voted 
tliat  their  ])ublication  should  be  discouraged  as  injurious  to 
science.  Tiiis  view  has  not,  however,  been  univei*sally  ac- 
cepted, and  three  values  of  the  solar  parallax  from  the  obser- 
vations of  the  transit  of  1874  have  already  appeared,  one  from 
the  French  and  two  from  the  English  observations.  The 
French  observations  here  referred  to  were  those  made  at  two 


SOLAR  PABALLAX  FROM  TRANSITS   OF  VENUS.        191 

stations,  Peking  and  St.  Paul's  Island.  They  were  calculated 
in  1875  by  M.  Pniseux,  a  member  of  the  French  Academy  of 
Sciences,  and  led  to  8".88  as  the  value  of  the  solar  parallax. 

The  British  observations  of  contacts  were  worked  up  under 
the  direction  of  Sir  George  Airy,  in  1877,  and  were  found  to 
lead  to  a  surprisingly  small  result,  8".76.  But  Mr.  E.  J.  Stone 
took  the  very  same  observations,  and,  by  treating  and  inter- 
preting them  in  a  different  way,  obtained  the  result  8".8S. 
Captain  G.  L.  Tupman,  who  had  superintended  the  reduction 
of  the  observations,  was  led  by  this  discordance  to  make  a  third 
combination.  He  found  8".857  from  the  observations  of  in- 
gress, and  8'^792  from  those  of  egress.  The  most  probable 
final  result  was  8'\S13.  That  results  so  different  could  be 
obtained  from  the  same  observations  must  cast  doubt  upon 
their  value,  and  raise  questions  which  can  be  decided  only  by 
the  combination  of  the  British  observations  with  those  made 
by  other  leading  governments. 

The  observations  of  the  transit  of  1882  were,  in  general, 
much  better  than  those  of  the  preceding  one.  One  reason  for 
this  w^as  that  the  experience  of  the  first  transit  was  available 
in  the  observations  of  the  second,  so  that  observers  knew  better 
what  they  were  to  look  for.  Another  reason  was  that  the 
weather  was  more  favorable  at  all  the  important  stations.  In 
1874  work  at  every  one  of  the  eight  American  stations  was 
interfered  with  more  or  less  by  clouds,  and  the  atmospheric 
conditions  were  especially  bad  for  photographing.  In  1882 
the  weather  was  everything  that  could  be  desired  at  the  sev- 
eral stations,  and  the  observations  were  not  entirely  lost  in  any 
case.  The  final  outcome  is  that,  while  only  some  two  hundred 
photographs  of  the  transit  of  1874  admitted  of  measurement, 
more  than  a  thousand  measurable  photographs  were  obtained 
in  1882. 

Notwithstanding  the  successful  observations  of  the  last  tran- 
sit, it  will  probably  be  found  that  the  uncertainty  of  the  results 
is  still  considerable,  and  that  this  method  is  not  the  most  ac- 
curate one  for  obtaining  the  solar  parallax.  AVe  have  already 
described  an  uncertainty  in  the  observations  of  the  older  tran- 

14. 


192  PRACTICAL  ASTRONOMY. 

sit,  arising  from  the  so-called  black  drop.  In  the  recent  ones 
it  was  found  that  this  disturbing  cause  could  be  avoided  by 
careful  attention  to  the  quality  of  the  image  formed  in  the 
telescope,  and  by  choosing  stations  where  the  sun  would  not  be 
too  near  the  horizon.  But  even  when  every  possible  precaution 
was  taken,  and  when  all  the  conditions  were  most  favorable,  it 
was  not  found  possible  to  make  observations  in  different  parts 
of  the  world  which  should  perfectly  correspond  to  each  other. 
Where  the  atmosphere  was  very  cleaj",  the  illuminated  limb  of 
Venus  off  the  sun's  disk  was  seen  before  first  internal  contact, 
and  sometimes  produced  doubt  in  the  mind  of  the  observer  as 
to  the  exact  time.  The  attention  of  astronomers  has  therefore 
been  called  to  other  methods  of  determining  the  sun's  distance, 
some  of  which  are  believed  to  be  more  accurate  than  transits 
of  Yen  us. 

§  4.   Other  Methods  of  determining  the  Suns  Distance^  and  their 

Results. 

The  methods  of  determining  the  astronomical  unit  which 
we  have  described  rest  entirely  upon  measures  of  parallax,  an 
angle  which  hardly  ever  exceeds  20",  and  which  it  is  there- 
fore exceedingly  difficult  to  measure  with  the  necessary  ac- 
curacy. If  there  were  no  other  way  than  this  of  determining 
the  sun's  distance,  we  might  despair  of  being  sure  of  it  with- 
in 200,000  miles.  But  the  refined  investigations  of  modern 
science  have  brought  to  light  other  methods,  by  at  least  two 
of  which  we  may  hope,  ultimately,  to  attain  a  greater  degree 
of  accuracy  than  we  can  by  measuring  parallaxes.  Of  these 
two,  one  depends  on  the  gravitating  force  of  the  sun  upon  the 
moon,  and  the  other  upon  the  velocity  of  light. 

Parallactic  Equation  of  the  Moon. — The  motion  of  the  moon 
around  the  earth  is  largely  affected  by  the  gravitating  force 
of  the  sun,  or,  to  speak  more  exacth^,  by  the  difference  of  the 
gravitating  force  of  the  sun  upon  the  moon  and  upon  the 
earth.  A  part  of  this  difference  depends  upon  the  ])roj)ortion 
between  the  respective  distances  of  the  moon  and  the  sun,  so 
that  when  this  force  is  known,  the  proportion  can  be  deter- 


METHODS  OF  DETERMINING  THE  SUN'S  DISTANCE.      195 

mined.  The  distance  of  the  moon  being  known  with  all  nec- 
essary precision,  we  have  only  to  multiply  it  by  the  proportion 
thus  obtained  to  get  the  distance  of  the  sun.  The  force  in 
question  shows  itself  by  producing  a  certain  inequality  in  the 
moon's  motion,  by  which  she  falls  two  minutes  behind  her 
mean  place  near  the  lirst  quarter,  and  is  two  minutes  ahead 
near  her  last  quarter.  In  determining  this  inequality,  we  have 
to  measure  an  angle  about  six  times  as  great  as  the  average 
of  the  planetary  parallaxes  on  which  the  sun's  distance  de- 
pends ;  so  that,  if  we  could  measure  both  angles  with  the  same 
precision,  the  error,  by  using  the  moon,  would  be  only  one- 
sixth  as  great  as  in  direct  measures  of  parallax.  But  it  seems 
as  if  nature  had  determined  to  allow  mankind  no  royal  road 
to  a  knowledge  of  the  sun's  distance.  It  is  the  position  of 
the  moon's  centre  which  we  require  for  the  purpose  in  ques- 
tion, and  this  can  never  be  directly  fixed.  We  have  to  make 
our  observations  on  the  limb  or  edge  of  the  moon,  as  illu- 
minated by  the  sun,  and  must  reduce  our  observations  to  the 
moon's  centre,  before  we  can  use  them.  The  worst  of  the 
inatter  is,  that  one  limb  is  observed  at  the  first  quarter,  and 
•another  at  the  third  quarter,  so  that  we  cannot  tell  with  abso- 
lute certainty  how  much  of  the  observed  inequality  is  real^ 
.'md  how  much  is  due  to  the  change  from  one  limb  to  the  other. 
So  great  is  the  uncertainty  here  that,  previous  to  1S54,  it  was 
supposed  tliat  the  inequality  in  question  was  about  122", 
agreeing  with  the  theoretical  inequality  from  Encke's  errone- 
ous value  of  the  solar  parallax.  Hansen  then  found  tliat  it 
was  really  about  4:"  greater,  and  thus  was  led  to  the  conclusion 
that  the  parallax  of  the  sun  must  be  increased,  and  his  distance 
diminished,  by  one-thirtieth  of  the  whole  amount. 

It  is  quite  likely  that  by  adopting  improved  modes  of  ob- 
servation, it  will  be  found  that  the  sun's  distance  can  be  more 
accurately  measured  in  this  way  than  through  tlie  parallaxes 
of  the  planets.  Some  pains  have  already  been  taken  to  deter- 
mine the  exact  amount  of  the  inequality  from  observations, 
the  result  being  125'^6.  The  entire  seconds  may  here  be  re- 
lied on,  but  the  decimal  is  quite  uncertain.     We  can  only  say 


196  PEACTICAL  ASTRONOMY. 

that  we  are  pretty  surely  -within  three  or  four  tenths  of  a  sec- 
ond of  the  truth.  From  this  vahie  the  paralkix  of  the  sun  ia 
found  to  be  S".83,  with  an  uncertainty  of  two  or  three  hun- 
dredths of  a  second. 

Suns  Distance  from  the  Velocity  of  Light.  —  There  is  an  ex- 
traordinary beauty  in  this  method  of  measuring  the  sun's  dis- 
tance, arising  from  the  contrast  between  the  simplicity  of  the 
principle  and  the  profoundness  of  the  methods  by  which  alone 
the  principle  can  be  applied.  Suppose  we  had  a  messenger 
whom  we  could  send  to  and  fro  between  the  sun  and  the 
earthj  and  who  could  tell,  on  his  return,  exactly  how  long  it 
took  him  to  perform  his  journey;  suppose,  also,  we  knew  the 
exact  rate  of  speed  at  which  he  travelled.  Then,  if  we  mul 
tiply  his  speed  by  the  time  it  took  him  to  go  to  the  sun,  wc 
shall  at  once  have  the  sun's  distance,  just  as  we  could  deter^ 
mine  the  distance  of  two  cities  when  we  knew  that  a  train 
running  thirt}'  miles  an  hour  required  seven  hours  to  pass  be- 
tween them.  Such  a  messenger  is  light.  It  has  been  found 
practicable  to  determine,  experimentally,  about  how  fast  light 
travels,  and  to  find  from  astronomical  phenomena  how  long 
it  takes  to  come  from  the  sun  to  the  earth.  How  these  de- 
terminations are  made  will  be  shown  in  the  next  chapter; 
here  we  shall  stop  only  to  give  results. 

In  1862  Foucault  found  by  experiment  that  light  travelled 
about  298,000  kilometres,  or  185,200  miles  per  second. 

In  1871:  Cornu  fonnd  by  a  different  series  of  experiments 
a  velocity  of  300,400  kilometres  per  second. 

In  1879  Ensign  A.  A.  Michelson,  U.  S.  Navy,  found  the  ve- 
locity to  be  299,910  kilometres  per  second. 

This  result  of  Michelson's  is  far  more  reliable  than  either 
of  the  preceding  ones.  Combining  them  all.  Professor  D.  P. 
Todd,  in  1880,  concluded  the  most  probable  value  of  the  ve- 
locity to  be  299,920  kilometres,  or  186,360  miles  per  second. 
Now,  we  know  from  the  phenomena  of  aberration,  hereafter 
to  be  described,  that  light  passes  from  the  sun  to  the  earth  in 
about  498  seconds.  The  product  of  these  two  numbers  gives 
the  distance  of  the  sun  in  miles.     Making  all  necessary  cor- 


METHOrS  OF  DETERMINING   THE  SUN'S  DISTANCE.      197 

rections,  and  using  Struve's  constant  of  aberration,  the  sun's 
parallax  was  found  by  Mr.  Todd  to  be  S''.811. 

These  two  methods  of  determining  the  distance  of  the  snn 
may  fairly  be  regarded  as  equal  in  accuracy  to  that  by  tran- 
sits of  Venus  when  they  are  enjployed  in  the  best  niannci*. 
There  are  also  two  or  three  minor  methods  which,  though 
less  accurate,  are  worthy  of  mention.  One  of  the  most  in- 
genious of  these  was  first  applied  by  Leverrier.  It  is  known 
from  the  theory  of  gravitation  that  the  eartli,  in  consequence 
of  the  attraction  of  the  moon,  describes  a  small  monthly  orbit 
around  the  common  centre  of  gravity  of  these  two  bodies,  cor- 
responding to  the  monthly  revolution  of  the  moon  around  the 
earth,  or,  to  speak  with  more  precision,  around  the  same  com- 
mon centre  of  gravity.  If  we  know  the  mass  (or  weight)  of 
the  moon  relatively  to  that  of  the  earth,  and  her  distance,  we 
can  thus  calculate  the  radius  of  the  little  orbit  referred  to. 
In  round  numbers,  it  is  3000  miles.  This  monthly  oscillation 
of  the  earth  will  cause  a  corresponding  oscillation  in  the  lon- 
gitude of  the  sun,  and  by  measuring  its  apparent  amount  we 
can  tell  how  far  the  sun  must  be  placed  to  make  this  amount 
correspond  to,  say  3000  miles.  Leverrier  found  the  oscilla- 
tions in  arc  to  be  6".50.  From  this  he  concluded  the  solar 
parallax  to  be  8".95.  But  Mr.  Stone,*  of  Greenwich,  found 
two  errors  in  Leverrier's  computation ,f  and,  when  these  are 
corrected,  the  result  is  reduced  to  8".85. 

Another  recondite  method  has  beeu  employed  by  Leverrier. 
It  is  founded  on  the  principle  that  when  the  relative  masses 
of  the  sun  and  earth  are  known,  their  distance  can  be  found 
by  comparing  the  distance  which  a  heavy  body  will  fall  in 
one  second  at  the  surface  of  the  earth  with  the  fall  of  the  lat- 
ter towards  the  sun  in  the  same  time.  The  mass  of  the  earth 
was  fonnd  by  its  disturbing  action  on  the  planets  Venus  and 
Mars,  as  explained  in  the  chapter  on  Gravitation.     Leverrier 

*  Mr.  E.  J.  Stone  was  then  first  assistant  at  the  Royal  Observatory,  Green- 
wich, but  has  teen  Astronomer  Royal  at  the  Cape  of  Good  Hope  since  1870. 

t  "Monthly  Notices  of  the  Royal  Astronomical  Society,"'  vol.  xxvii.,  p,  241, 
and  vol.  xxviii.,  pp.  22,  23. 


198  PRACTICAL  ASTRONOMY. 

concluded  that  this  method  gave  the  value  of  the  solar  paraU 
lax  as  8".S6.  But  one  of  his  numbers  requires  a  small  correc- 
tion, which  reduces  it  to  8".83.  Another  determination  of  the 
mass  of  the  earth  relative  to  that  of  the  snn  has  recently  been 
made  by  Yon  Asten,  of  Pulkowa,  f rom  the  action  of  the  earth 
upon  Encke's  comet.  The  solar  parallax  thence  resulting  is 
9".009,  the  largest  recent  value;  but  the  anomalies  in  the  ap- 
parent motions  of  this  comet  are  such  that  very  little  reliance 
can  be  placed  upon  this  result. 

Yet  another  method  of  determining  the  sclar  parallax  has 
been  proposed  and  partially  carried  out  by  Dr.  Galle.*  It 
consists  in  measuring  the  parallax  of  some  of  the  small  plan- 
ets between  Mars  and  Jupiter  at  the  times  of  their  nearest 
approach  to  the  earth,  by  observations  in  the  northern  and 
southern  hemispheres.  The  least  distance  of  the  nearest  of 
these  bodies  from  us  is  little  less  than  that  of  the  sun,  so  that 
in  this  respect  they  are  far  less  favorable  than  Yenus  and 
Mars.  But  they  have  the  great  advantage  of  being  seen  in 
the  telescope  only  as  points  of  light,  like  stars,  and,  in  conse- 
quence, of  having  their  position  relative  to  the  surrounding 
stars  determined  with  greater  precision  than  can  be  obtained 
in  the  case  of  disks  like  those  of  Yenus  and  Mars.  Observa- 
tions of  Flora  were  made  in  this  way  at  a  number  of  observa- 
tories in  both  hemispheres  during  the  opposition  of  1874,  from 
which  Dr.  Galle  has  deduced  8".875  as  the  value  of  the  solar 
parallax. 

3Iost  Probable  Value  of  the  Sufi's  Parallax. — It  will  be 
seen  that,  although  many  of  the  preceding  i-esults  are  dis- 
cordant, those  wliicli  are  most  reliable  generally  fall  between 
the  limits  8".76  and  8".85.  Taking  them  all  into  considera- 
tion, there  can  be  no  reasonable  doubt  tliat  the  parallax  lies 
between  the  limits  8".78  and  8". 82.  We  may  therefore  say 
that  the  most  probable  value  of  the  sun's  parallax  is  8''.80, 
but  this  result  is  still  subject  to  an  uncertainty  of  two-hun- 

*  Dr.  J.  G.  Galle,  now  director  of  the  observatory  at  Breslau,  Eastern  Prussia. 
He  was  formerly  assistant  at  the  Observatory  of  Berlin,  where  he  became  cele- 
brated as  the  optical  discoverer  of  the  planet  Neptune. 


STELLAR  PARALLAX.  199 

dredths  of  a  second,  or  we  might  say  an  uncertainty  of  -^ 
of  its  whole  amount.  Translated  into  distance,  we  may  piace 
the  distance  of  the  sim  between  the  limits  92,500,000  and 
93,000,000  of  miles.  We  may,  therefore,  call  the  distance  of 
the  sun  92f  millions  of  miles,  with  the  uncertainty,  perhaps, 
of  nearly  one  quarter  of  a  million.  Within  the  next  ten  years 
we  may  hope  to  see  the  result  fixed  with  greater  certainty,  but 
this  is  as  near  as  we  can  approach  it  in  the  present  state  of 
astronomy. 

In  many  recent  works  the  distance  in  question  will  be  found 
stated  at  91,000,000  and  some  fraction.  This  arises  from  the 
circumstance  that  into  several  of  the  first  determinations  by 
the  new  methods  small  errors  and  imperfections  crept,  which, 
by  a  singular  coincidence,  all  tended  to  make  the  parallax  too 
great,  and  therefore  the  distance  too  small.  For  instance, 
Hansen's  original  computions  from  the  motion  of  the  moon, 
led  liini  to  a  parallax  of  S".9C\  This  result  has  been  proved 
to  be  too  large  from  various  causes. 

The  observations  of  Mars,  in  1862,  as  reduced  by  Winnecke 
and  Stone,  first  led  to  a  parallax  of  8''.92  to  8''.94,  But  in 
these  investigations  only  a  small  portion  of  the  obsf/vations 
was  used.  When  the  great  mass  remaining  was  joined  with 
them,  the  result  was  8".85. 

The  early  determinations  of  the  time  required  for  light  to 
come  from  the  sun  were  founded  on  the  extremely  uncertain 
observations  of  eclipses  of  Jupiter's  satellites,  and  were  five  to 
six  seconds  too  small.  The  time,  493  seconds,  being  used  in 
some  computations  instead  of  498  seconds,  the  distance  of  the 
sun  from  the  velocity  of  light  was  made  too  small. 

In  both  of  Leverrier's  methods  some  small  errors  of  computa- 
tion have  been  found,  the  effect  of  all  of  which  is  to  make  his 
parallax  too  great.  Correcting  these,  and  making  no  change  in 
any  of  his  data,  the  results  are  respectively  8".S5  and  8".83. 

§  5.  Stellar  Parallax. 

It  is  probable  that  no  one  thing  tended  more  strongly  to 
impress  the  minds  of  thoughtful  men  in  former  times  with 


200  PRACTICAL  ASTRONOMY. 

tjie  belief  that  the  earth  was  immovable  than  did  the  absence 
of  stellar  parallax.  We  may  call  to  mind  that  the  annual  par- 
allax of  the  fixed  stars  arises  from  the  change  in  their  direc- 
tion produced  by  the  motion  of  the  earth  from  one  side  of 
its  orbit  to  the  other.  One  of  the  earliest  forms  in  which  wo 
may  suppose  this  parallax  to  have  been  looked  for  is  shown 
in  Fig.  56.     Suppose  AB  to  be  the  earth's  orbit  with  the  sun, 


Fio.  56.— Effect  of  stellar  parallax. 

S,  near  its  centre,  and  RT  two  stars  so  situate(!i  as  to  be  direct- 
ly opposite  each  other  when  the  earth  is  at  A ;  that  is,  when 
the  direction  of  each  star  is  90°  distant  from  that  of  the  sun. 
Then  it  is  clear  that,  after  six  months,  when  the  earth  is  at  B^ 
the  stars  will  no  longer  be  opposite  each  other,  the  point  U, 
which  is  opposite  i?,  making  the  angle  TBU,  with  the  direc- 
tion of  T.  The  stars  will  all  be  displaced  in  the  same  direc- 
tion that  the  sun  is  in  from  the  earth.  When  it  was  found 
that  the  most  careful  observations  showed  no  such  displace- 
ment, the  conclusion  that  the  earth  did  not  move  seemed  in- 
evitable. We  have  seen  how  Tycho  was  led  in  this  way  to 
reject  the  doctrine  of  the  earth's  motion,  and  favor  a  system 
in  which  the  sun  moved  around  it.  In  this  Tycho  was  fol- 
lowed by  the  ecclesiastical  astronomers  who  lived  during  the 
seventeenth  century,  and  who,  finding  no  parallax  whatever  to 
any  of  the  stars,  were  led  to  reject  the  Copernican  system. 

The  telescope  furnishing  so  powerful  an  auxiliary  in  meas- 
uring small  angles,  it  was  natural  that  the  defenders  of  the 
Copernican  system  should  be  anxious  to  employ  it  in  detect- 
ing the  annual  parallax  of  the  stars.  But  the  earlier  observ- 
ers had  very  imperfect  notions  of  the  mechanical  appliances 
necessary  to  do  this  with  success,  and,  in  consequence,  the  in- 
vention of  the  telescope  did  not  result  in  any  immediate  ira- 


STELLAR  PARALLAX.  201 

provement  in  the  methods  of  celestial  measurement.  A  step 
was  taken  in  16G9  by  Hooke,  of  England,  who  was  among  the 
first  to  see  how  the  telescope  was  to  be  applied  in  the  meas- 
urement of  the  apparent  distances  of  the  stars  from  the  ze- 
nith. He  fixed  a  telescope  thirty-six  feet  long  in  his  house,  in 
a  vertical  position,  the  object-glass  being  in  an  opening  in  the 
roof,  while  the  eye-piece  was  in  one  of  the  lower  rooms.  A 
fine  plnmb-line  hung  down  from  the  object-glass  to  a  point 
below  the  eye -piece,  which  gave  a  truly  vertical  line  from 
which  to  measure.  The  star  selected  for  observation  was  y 
Draconis,  because  it  was  comparatively  bright,  and  passed  over 
the  zenith  of  London.  His  mode  of  observation  was  to  meas- 
ure the  distance  of  the  image  of  the  star  from  the  plumb-line 
from  day  to  day  at  the  moment  of  its  passing  the  meridian. 
He  had  made  but  four  observations  when  his  object-glass  wa? 
accidentally  broken,  and  the  attempt  ended  without  leading 
to  any  result  whatever. 

Between  1701  and  1704,  Roomer,  then  of  Copenhagen,  at- 
tempted to  determine  the  sum  of  the  double  parallaxes  of 
Sirius  and  a  L3'rse  by  the  principle  shown  in  Fig.  58.  These 
stars  lie  somewhere  near  the  opposite  quarters  of  the  celestial 
sphere,  and  the  angle  between  them  will  vary  from  spring  to 
autumn  by  nearly  double  the  sum  of  their  parallaxes.  The 
angle  was  measured  by  the  transit  instrument  and  the  astro- 
nomical clock,  by  noting  the  time  which  elapsed  between  the 
transit  of  Sirius  over  the  meridian,  and  that  of  a  Lyrce.  This 
time  was  found  to  be,  on  the  average, 

Hrs.    Min.       Ser. 

In  February,  March,  and  April 11     54     r>9. 7 

In  September  and  October 11     54    55.4 

Diiference 4.3 

Here  was  a  difference  of  four  seconds  of  time,  or  a  minute  of 
angle,  which  was  then  very  naturally  attributed  to  the  motion 
of  the  earth,  and  which  was  afterwards  printed  in  a  disserta- 
tion entitled  "  Copernicus  Triumphans."  It  is  now  known  that 
there  is  no  such  parallax  as  this  to  either  of  these- stars,  and 


202  PRACTICAL  ASTRONOMY. 

Peters*  has  shown  that  the  difference  which  was  attributed 
to  parallax  by  the  enthusiastic  Danish  astronomers  really  arose, 
in  great  part,  from  the  diurnal  ii-regularity  in  the  rate  of  their 
clock,  caused  by  the  action  of  the  diurnal  change  of  tempera- 
ture upon  the  uncompensated  pendulums.  In  the  spring  the 
interval  of  time  measured  elapser"  during  the  night,  Sirius 
passing  the  meridian  in  the  evening,  and  a  Lyrae  in  the  morn- 
ing. The  cold  of  night  made  the  clocks  go  too  fast,  and  so 
the  measured  interval  came  out  too  great.  In  the  autumn 
Sirius  passed  in  the  morning,  and  a  Lyrse  in  the  evening ;  the 
clock  was  going  too  slow  on  account  of  the  heat  of  the  day, 
and  the  interval  came  out  too  small. 

Among  the  numerous  other  vain  efforts  made  by  the  astron- 
omers of  the  last  century  to  detect  the  stellar  parallax,  that  of 
Bradley  is  worthy  of  note,  owing  to  the  remarkable  discovery 
of  the  aberration  of  light  to  which  it  led.  The  principle  of 
his  instrument  was  the  same  as  that  of  Hooke,  the  zenith  dis- 
tance of  the  star  -y  Draconis  at  the  moment  of  its  passing  the 
meridian  being  determined  by  the  inclination  of  a  telescope  to 
a  fine  plumb-line.  The  instrument  thus  used,  which  has  be- 
come so  celebrated  in  the  history  of  astronomy,  ha»  since  been 
known  as  Bradley's  zenith  sector.  In  accuracy  it  was  a  long 
step  in  advance  of  any  which  preceded  it,  so  that  by  its  means 
Bradley  was  able  to  announce  with  certainty  that  the  star  in 
question  had  no  parallax  approaching  a  single  second.  But 
lie  found  another  annual  oscillation  of  a  very  remarkable 
character,  arisiTig  from  the  progressive  motion  of  light,  which 
will  be  described  in  the  next  chapter.  It  has  frequently  hap- 
pened in  the  history  of  science  that  an  investigation  of  some 
cause  has  led  to  discoveries  in  a  different  direction  of  an  en- 
tirely unexpected  character. 

It  would  be  tedious  to  describe  in  detail  all  the  efforts 
made  by  astronomers,  during  the  last  centuiy  and  the  early 
part  of  the  present  one,  to  detect  the  stellar  parallax.     It  will 


*  C.  A.  F.  refers,  tlieu  of  the  Pulkowa  Observatory,  the  late  editor  of  the  As' 
tronomische  Nachrichten, 


STELLAR  PARALLAX.  203 

be  sufficient  to  say,  in  a  general  way,  that  they  depended  on 
absolute  measures ;  that  is,  the  astronomer  endeavored,  gen- 
erally by  a  divided  circle,  to  determine  from  day  to  day  the 
zenith  distance  at  which  the  star  passed  the  meridian.  The 
position  of  tlie  zenith  was  determined  in  various  ways — some- 
times by  a  fine  plumb-line,  sometimes  by  the  level  of  quick- 
silver. What  is  required  is  the  angle  between  the  plumb-line 
and  the  line  of  sight  from  the  observer  to  the  star.  The  same 
result  can  be  obtained  by  observing  the  angle  between  a  ray 
coming  directly  from  a  star  and  the  ray  which,  coming  from 
the  star,  strikes  the  surface  of  a  basin  of  quicksilver,  and  is  re- 
flected upwards.  Whatever  method  is  used,  a  large  angle  has 
to  be  measured,  an  operation  which  is  always  affected  by  un- 
certainty, owing  to  the  influences  of  varying  temperatures  and 
many  other  causes  upon  the  instrument.  The  general  result 
of  all  the  efforts  made  in  this  way  was  that  while  several  oi 
the  brighter  stars  seemed  to  some  astronomers  to  have  paral- 
laxes, sometimes  amounting  to  two  or  three  seconds,  though 
generally  not  much  exceeding  a  second,  yet  there  was  no  such 
agreement  between  the  vai-ious  results  as  was  necessary  to  in- 
spire confidence.  As  a  matter  of  fact,  we  now  know  that 
these  results  were  entirely  illusory,  being  due,  not  to  parallax, 
but  to  the  unavoidable  errors  of  the  instruments  used. 

Struve  was  the  first  one  to  prove  conclusively  that  the  par- 
allaxes even  of  the  brighter  stars  were  so  small  as  to  abso- 
lutely elude  every  mode  of  measurement  before  adopted.  In 
principle  his  method  was  that  employed  by  Roemer,  the  sum 
of  the  parallaxes  of  stars  twelve  hours  distant  in  right  ascen- 
sion being  determined  by  the  annual  change  in  the  inteiwals 
between  their  times  of  transit  over  the  meridian.  But  he 
made  the  great  improvement  of  selecting  stai's  which  could 
be  observed  as  they  passed  the  meridian  below  the  pole,  as 
well  as  al)Ove  it,  so  that  a  short  time  before  or  after  observing 
the  transit  of  a  star  he  could  turn  his  transit  instrument  be- 
low the  pole,  and  observe  the  transit  of  the  opposite  star  from 
west  to  east.  Thus  he  was  not  under  the  necessity  of  depend- 
ing on  the  rate  of  his  clock  for  more  than  an  hour  or  two, 


204  PRACTICAL  ASTEOXOMT. 

while  Roemer  had  to  depend  on  it  for  twelve  hours.  The  re- 
sult of  Strnve  was  that  the  average  parallax  of  the  tweiit}*- 
five  brightest  stai-s  within  45°  of  the  pole  could  not  much,  if 
at  all,  exceed  a  single  tenth  of  a  second. 

Such  was  the  general  state  of  things  up  to  the  year  1835. 
It  was  then  decided  by  Struve  and  Bessel,  in  lieu  of  attempt- 
ing to  determine  zenith  distances,  to  adopt  the  method  of 
relative  parallaxes.  The  idea  of  this  method  really  dates  al- 
most from  the  invention  of  the  telescope.  It  was  considered 
bv  Galileo  and  Iluyghens  that  where  a  bright  and  a  faint 
star  were  seen  side  by  side  in  the  field  of  view  of  a  telescope, 
the  latter  was  probably  vastly  more  distant  than  the  former, 
and  that  consequently  they  would  change  their  relative  po- 
sition as  the  earth  moved  from  one  side  of  the  sun  to  the  oth- 
er. If,  for  instance,  one  star  was  three  times  the  distance  of 
the  other,  its  apparent  motion  produced  by  parallax  would  be 
only  a  third  that  of  the  other,  and  there  would  remain  a  rel- 
ative parallax  equal  to  two-thirds  that  of  the  brighter  star, 
which  could  be  detected  by  measuring  the  angular  distance 
of  the  two  stars  as  seen  in  the  telescope  from  day  to  day 
throughout  the  vear.  The  drawback  to  which  this  method  is 
subject  is  the  impossibility  of  determining  how  many  times 
farther  the  one  star  is  than  the  other ;  in  fact,  it  may  be  that 
the  smaller  star  is  really  no  farther  than  the  large  one.  No 
doubt  it  was  this  consideration  which  deterred  the  astrono- 
mers of  the  last  century  from  trying  this  very  simple  method. 

The  astronomers  of  the  last  generation  found  cases  in 
which  there  could  be  little  doubt  that  a  star  was  much  near- 
er to  us  than  the  small  stars  which  surrounded  it  in  the  field 
of  the  telescope.  For  instance,  the  star  61  Cygni,  or  rather 
the  pair  of  stars  thus  designated,  are  found  not  to  occupy  a 
fixed  position  in  the  celestial  sphere,  like  the  surrounding 
small  stars,  but  to  be  moving  forward  in  a  straight  line  at  the 
rate  of  six  seconds  per  year.  This  amount  of  proper  motion 
was  so  unusual  as  to  make  it  probable  that  the  star  must  be 
one  of  the  nearest  to  us,  although  it  was  only  of  the  sixth  mag- 
nitude.    It  Avas  therefore  selected  by  Eessel  for  the  investi- 


STELLAR  PARALLAX.  205 

gation  of  its  parallax  relative  to  two  other  stars  in  its  neigli- 
borliood.  The  instrument  used  was  the  helioraeter,  an  in- 
strument which,  as  now  made,  admits  of  great  precision,  but 
which  was  then  liable  to  small  uncertainties  from  various 
causes.  His  early  attempts  to  detect  a  parallax  failed  as 
completely  as  had  those  of  former  observers.  He  recom- 
menced them  in  August,  1837,  his  first  series  of  measures  be- 
ing continued  until  October,  1838.  The  result  of  this  series 
was  the  detection  of  a  parallax  of  about  three-tenths  of  a  sec- 
ond (0".3136).  He  then  took  down  his  instrument,  made  some 
improvements  in  it,  and  commenced  a  second  series,  which  he 
continued  until  July,  1839  ;  and  his  assistant,  Schliiter,  until 
March,  1840.  The  final  value  of  the  parallax  deduced  by 
Bessel  froni  all  these  observations  was  0''.35.  The  reality  of 
this  parallax  luii  been  well  established  by  subsequent  investi- 
gators, only  it  has  been  found  to  be  a  little  larger.  From  a 
combination  of  all  the  results,  Auwers,  of  Berlin,  finds  the 
most  probable  parallax  to  be  0".51. 

The  star  selected  by  Stru\  e  for  the  measure  of  relative  par- 
allax was  the  bright  one  a  Lyrse.  This  has  not  only  a  sensible 
proper  motion, but  is  of  the  first  magnitude;  so  that  there  is 
every  reason  to  believe  it  to  be  among  those  which  are  nearest 
to  us.  The  comparison  was  made  witli  a  single  very  small 
star  in  the  neighborhood,  the  instrument  used  being  the  nine- 
inch  telescope  of  the  Dorpat  Observatory.  The  observations 
extended  from  November,  1835,  to  August,  1838.  The  result 
was  a  relative  parallax  of  a  quarter  of  a  second.  Subsequent 
investigations  have  reduced  this  parallax  to  two-tenths  of  a 
second,  so  that  although  a  Lyra3  is  nearly  a  hundred  times  as 
bright  as  either  of  the  pair  of  stars  61  Cygni,  it  is  more  than 
twice  as  far  from  us. 

Before  the  publication  of  these  works  of  Struve  and  Bessel 
it  w-as  found  by  Henderson,  the  Englisli  astronomer  at  the 
Cape  of  Good  Hope,  that  the  star  a  Centauri  had  a  parallax 
of  about  one  second.  This  result  has  been  confirmed  by  re- 
cent measures,  except  that  the  parallax  is  found  to  be  only 
three-fourths  of  a  second ;  and  it  is  now  well  established  that 


206  PRACTICAL  ASTEOXOMY. 

a  Centaini  is,  so  far  as  can  be  learned,  the  nearest  of  all  the 
fixed  stars.  Being  in  60°  south  declination,  this  star  is  not 
visible  in  our  latitudes. 

In  lS-i2-43  most  elaborate  observations  of  a  number  of 
stare,  with  the  view  of  detecting  their  parallax,  were  iriade 
at  the  Pulkowa  observatory  by  Dr.  C.  A.  F.  Peters.  All  the 
parallaxes  he  detected  were  small  and  doubtful.  He  meas- 
ured the  absolute  declination  of  each  star  from  time  to  time, 
instead  of  its  distance  from  some  small  star  near  it,  a  method 
which  has  not  since  been  applied,  owing  to  its  uncertainty. 

The  next  attempt  to  determine  the  parallaxes  of  a  number 
of  stars  on  a  uniform  plan  was  commenced  by  Dr.  BrUnnow, 
at  Dublin,"  aiid  continued  by  his  successor.  Sir  Robert  S.  Ball. 
Neither  of  them  has  found  any  stars  with  a  large  parallax. 

The  most  recent  and  elaborate  determinations  of  stellar 
parallax  have  been  made  at  the  Cape  of  Good  Hope  by  Dr. 
David  Gill,  her  Majesty's  astronomer  at  that  place,  and  Dr. 
W.  L.  Elkin,  now  of  the  Tale  College  observatory-.  Their  in- 
strument was  a  heliometer,f  constructed  by  the  Repsolds  for 
Lord  Lindsay's  expedition  to  observe  the  transit  of  Venus  in 
1874. 

The  recent  determinations  of  stellar  parallax  by  Professor 
A.  Hall  should  also  be  mentioned.  They  were  made  with  the 
great  Washington  telescope.  Among  their  results  is  that  the 
parallax  of  Aldebaran,  which  was  supposed  to  be  among  the 
largest,  is  too  small  for  accurate  measurement. 

The  general  result  of  all  the  measures  of  stellar  parallax 
yet  made  may  be  very  briefly  summed  up.  The  distances  to 
be  given  so  transcend  all  our  ordinary  ideas  that  we  must  take 
as  a  unit  of  measure  the  distance  which  light  would  travel  in 
one  year,  which  is  about  237,000,000  times  the  circumference 
of  the  earth. 


*  Dr.  BrQnnow  was   formerly  director   of  the   observatory  of  Ann  Arbor, 
Michigan, 
f  See  the  glossaiy  in  the  Appendi.x  for  a  definition  of  this  instrument. 


STELLAR  PARALLAX.  207 

The  nearest  star,  a  Centani-i,  lias  a  parallax  of  0".To  and 
a  distance  of  four  and  a  half  light-units. 

Two  other  stars,  01  Cvgui  and  Lalande  211S5,  have  a  par- 
allax of  about  half  a  second  and  a  distance  of  seven  light- 
units. 

About  twelve  stars  have  parallaxes  ranging  from  0",i  to 
0".3,  and  distances  ranging  from  ten  to  thirty  light-units. 

Most  of  the  other  stars,  even  the  majority  of  those  of  tlie 
first  and  second  magnitudes,  are  so  distant  that  no  parallax 
has  yet  been  detected. 

The  absence  of  measurable  parallax  in  some  of  the  bright- 
est of  the  stars,  and  its  presence  in  some  very  small  ones,  is 
one  of  the  remarkable  features  of  the  starry  univei'se.  For 
example,  Canopus,  a  star  visible  in  more  soutliern  latitudes 
than  ours,  is  the  second  brightest  star  in  the  heavens.  .Drs. 
Gill  and  Elkin  found  a  parallax  of  only  0".03,  which  would 
give  a  distance  of  more  than  one  hundred  light-units.  The 
brilliancy  of  stars  varying  as  the  inverse  square  of  their  dis- 
tances, it  follows  that  if  Canopus  were  brought  as  near  us  as 
61  Cygni  is,  its  brightness  would  be  increased  some  two.  hun- 
dred times,  which  would  make  it  one  hundred  times  as  bright 
as  Sirius,  and  ten  thousand  times  as  bright  as  61  Cvsni. 

In  measurements  of  the  annual  parallax  of  the  Hxed  stars, 
it  sometimes  happens  t-hat  the  astronomer  finds  his  observa- 
tions to  give  a  negative  parallax.  To  understand  what  this 
means,  we  remark  that  a  determination  of  tlie  distance  of  a 
star  is  made  by  determining  its  directions,  as  seen  fi-om  oppo- 
site points  of  the  earth's  orbit.  If  we  draw  a  line  from  each 
of  these  points  in  the  observed  direction  of  the  star,  the  point 
in  which  the  lines  meet  marks  the  position  of  the  star.  A 
negative  parallax  shows  that  the  two  lines,  instead  of  converg- 
ing to  a  point,  actually  diverge,  so  that  there  is  no  possible 
position  of  the  star  to  correspond  to  the  observations.  Such  a 
paradoxical  result  can  arise  only  from  errors  of  observations. 

15 


208  FBACIICAL  ASTBOXOMY, 


CHAPTER  IV. 

THE   MOTION    OF    LIGHT. 

Intimately  connected  with  celestial  measurements  are  the 
curious  phenomena  growing  out  of  the  progressive  move- 
ment of  light.  It  is  now  known  that  when  we  look  at  a  star 
we  do  not  see  the  star  that  now  is,  but  the  star  that  was  sev- 
eral years  ago.  Though  the  star  should  suddenly  be  blotted 
out  of  existence,  we  should  still  see  it  shining  for  a  number 
of  years  before  it  would  vanish  from  our  sight.  We  should 
see  an  event  that  was  long  past,  perhaps  one  that  was  past 
before  we  were  born.  This  non-coincidence  of  the  time  of 
perception  with  that  of  occurrence  is  owing  to  the  fact  that 
Hght  requires  time  to  travel.  TVe  can  see  an  object  only  by 
light  which  emanates  from  it  and  reaches  our  eye,  and  thus 
our  sight  is  behind  time  by  the  interval  required  for  the  light 
to  travel  over  the  space  which  separates  us  fi'om  tlie  object. 

It  was  by  observations  of  the  satellites  of  Jupiter  that  it 
was  first  found  that  celestial  plienomena  wei-e  thus  seen  be- 
hind time.  These  bodies  revolve  round  Jupiter  much  more 
rapidly  than  our  moon  does  around  the  earth,  the  inner  satel- 
lite making  a  complete  revolution  in  eighteen  hours.  Owing 
to  the  great  magnitude  of  Jupiter  and  his  shadow,  this  satel- 
lite, as  also  the  two  next  outside  of  it,  are  eclipsed  at  every  rev- 
olution. The  accuracy  with  which  the  times  of  disappearance 
in  the  shadow  could  be  observed,  and  the  consequent  value  of 
such  observations  for  the  determination  of  longitudes,  led  the 
astronomers  of  the  seventeenth  century  to  make  tables  of  the 
times  of  occurrence  of  these  eclipses.  In  attempting  to  im- 
prove the  tables  of  his  predecessors,  it  was  found  by  Eoemer 
(then  of  Paris,  though  a  Dane  by  birth)  that  the  times  of  the 


THE  MOTION  OF  LIGHT.  209 

eclipses  could  not  be  represented  by  an  equable  motion  of 
the  satellites.  He  could  easily  represent  the  times  of  the 
eclipses  when  Jupiter  was  in  opposition  to  the  sun,  and  there- 
fore the  earth  nearest  to  Jupiter.  But  then,  as  the  earth  re- 
ceded from  Jupiter  in  its  annual  course  round  the  sun,  the 
eclipses  were  constantly  seen  later,  until,  when  it  was  at  its 
greatest  distance  from  Jupiter,  the  times  appeared  to  be  22 
minutes  late.  Such  an  inequality,  Roemer  concluded,  could 
not  be  real ;  he  therefore  attributed  it  to  the  fact  that  it  must 
take  time  for  light  to  come  from  Jupiter  to  the  earth,  and 
that  this  time  is  greater  tlie  more  distant  the  earth  is  from 
the  planet.  He  therefore  concluded  that  it  took  light  22 
minutes  to  cross  the  orbit  of  the  earth,  and,  consequently,  11 
minutes  to  come  from  the  sun  to  the  earth. 

The  next  great  step  in  the  theory  of  the  progressive  motion 
of  light  was  made  by  the  celebrated  Bradley,  afterwards  As- 
tronomer Royal  of  England,  to  wliose  observations  at  Kew  on 
the  star  -y  Draconis  with  his  zenith  sector,  in  order  to  deter- 
mine tlie  parallax  of  the  star,  allusion  has  already  been  made. 
The  effect  of  parallax  would  ha^•e  been  to  make  the  declina- 
tion greatest  in  June  and  least  in  December;  while  in  March 
and  September  the  star  would  occupy  an  intermediate  or 
mean  position.  But  the  actual  result  of  the  measures  was 
entirely  different,  and  exhibited  phenomena  w'hich  Bradley 
could  not  at  first  account  for.  The  declinations  of  June  and 
December  were  the  same,  showing  no  effect  of  parallax.  But, 
instead  of  remaining  the  same  the  rest  of  the  year,  the  decli- 
nation was  some  forty  seconds  greater  in  September  than  in 
March,  when  the  effect  of  parallax  should  be  the  same.  Thus, 
the  star  had  a  regular  annual  oscillation;  but  instead  of  its 
apparent  motion  in  this  little  orbit  being  opposite  to  tliat  of 
the  earth  in  its  annual  orbit,  as  required  by  the  laws  of  rela- 
tive motion,  it  was  constantly  at  right  angles  to  it. 

After  long  consideration,  Bradley  saw  the  cause  of  the 
phenomenon  in  the  progressive  motion  of  light  combined 
with  the  motion  of  the  earth  in  its  orbit.  In  Fig.  57  let  /S 
be  a  star,  and   OT  a  telescope  pointed  at  it.     Then,  if  the 


210  PRACTICAL  ASTRONOMY. 

telescope  is  not  in  motion,  the  ray  SOT  emanating  from  the 
star,  and  entering  the  centre  of  the  object-glass, 
will  pass  down  near  the  right-hand  edge  of  the  eye- 
piece, and  the  star  will  appear  in  the  right  of  the 
field  of  view.  But,  instead  of  being  at  rest,  all  our 
telescopes  are  carried  along  with  the  earth  in  its 
orbit  ronnd  the  sun  at  the  rate  of  nearh'  nineteen 
miles  a  second.  Suppose  this  motion  to  be  in  the 
direction  of  the  arrow ;  then,  while  the  ray  is  pass- 
ing down  the  telescope,  the  latter  moves  a  short  dis- 
tance, so  that  the  ray  no  longer  strikes  the  right- 
hand  edge  of  the  eye-piece,  but  some  point  farther 
to  the  left,  as  if  the  star  were  in  the  direction  S', 
and  the  ray  followed  the  course  of  the  dotted  line. 
In  order  to  see  the  star  centrally,  the  eye  end  of  the 
telescope  must  be  dropped  a  little  behind,  so  that. 

Fig.  57.  —  i^stcad  of  pointing  in  the  direction  S,  it  will  really 
Aberration  \)q  pointing  in  the  direction  S',  shown  bv  tiie  dotted 

of  light.  _,,   .  .n       1  ,  "  T 

ray.  Ihis  will  then  represent  the  apparent  direc- 
tion of  the  star,  which  will  seem  displaced  in  the  direction  in 
which  the  earth  is  moving. 

The  phenomenon  is  quite  similar  to  that  presented  by  the 
apparent  direction  of  the  wind  on  board  a  steamship  in  mo- 
tion. If  the  wind  is  really  at  right  angles  to  the  course  of  the 
ship,  it  will  appear  more  nearlj^  ahead  to  those  on  board ;  and 
if  two  ships  are  passing  each  other,  they  will  appear  to  have 
the  wind  in  different  directions.  Indeed,  it  is  said  to  have 
been  through  noticing  this  very  result  of  motion  on  board  a 
boat  on  the  Thames,  that  the  cause  of  the  phenomenon  he 
had  observed  was  suggested  to  Bradley. 

The  displacement  of  the  stars  which  we  have  explained  is 
called  the  Aberration  of  Light.  Its  amount  depends  on  the  I'a- 
tio  of  the  velocity  of  the  earth  in  its  orbit  to  the  velocity  of 
light.  It  can  be  determined  by  observing  the  declination  of 
a  star  at  the  proper  seasons  during  a  number  of  years,  by 
which  the  annual  displacement  will  be  shown.  The  value 
now  most  generally  received  is  that  determined  by  Struve  at 


THE  MOTION  OF  LIGHT.  211 

the  Pnlkowa  Observatory,  and  is  20".445.  Though  this  is  the 
most  rehable  vahie  yet  found,  the  two  last  figures  ai'e  both 
uncertain.  We  can  say  little  more  than  that  the  constant 
probably  hes  between  20".43  and  20".48,  and  that,  if  outside 
these  limits  at  all,  it  is  certainly  very  little  outside. 

This  amount  of  aberration  of  each  star  shows  that  light 
travels  10,089  times  as  fast  as  the  earth  in  its  orbit.  From 
this  we  can  determine  the  time  light  takes  to  travel  from  the 
sun  to  the  earth  entirely  independent  of  the  satellites  of  Ju- 
piter. The  earth  makes  the  circuit  of  its  orbit  in  365^  days. 
Then  light  would  make  this  same  circuit  in  \%'ll^  of  a  day, 
which  we  find  to  be  52  minutes  ^h,  seconds.  The  diameter 
of  the  earth's  orbit  is  found  by  dividing  its  circumference  by 
3.1416,  and  the  mean  distance  of  the  sun  is  half  this  diameter. 
We  thus  find  from  the  above  amount  of  aberration  that  light 
passes  from  the  sun  to  the  earth  in  8  minutes  18  seconds. 

The  question  now  arises.  Does  the  same  result  follow  from 
the  observations  of  the  satellites  of  Jupiter?  If  it  does,  we 
have  a  striking  confirmation  of  the  astronomical  theory  of  the 
propagation  of  light.  If  it  does  not,  we  have  a  discrepancy, 
the  cause  of  whicli  must  be  investigated.  We  have  said  that 
the  first  investigator  of  the  subject  found  the  time  required 
to  be  11  minutes.  This  determination  was,  however,  uncertain 
by  several  minutes,  owing  to  the  very  imperfect  character 
of  the  early  observations  on  which  Roemer  haa  i^j  depend. 
Early  in  the  present  century,  Delambre  made  a  complete  in- 
vestigation from  all  the  eclipses  of  the  satellites  which  had 
been  observed  between  1662  and  1802,  more  than  a  thousand 
in  number.     His  result  was  8  minutes  13.2  seconds. 

There  is  a  discrepancy  of  five  seconds  between  this  result 
of  Delambre,  obtained  some  seventy  years  ago,  and  the  mod- 
ern determinations  of  the  aberrations  of  the  fixed  stars  made 
by  Struve  and  others.  What  is  its  cause  ?  Probably  only  the 
errors  of  the  observations  used  by  Delambre.  In  this  case, 
there  would  be  no  real  difference.  But  some  physicists  and 
astronomers  have  endeavored  to  show  that  there  is  a  real 
cause  for  such  a  difference,  which  they  hold  to  indicate  an  er- 


212  PRACTICAL  ASTRONOMY. 

ror  ill  the  value  of  the  aberration  derived  from  observation 
arising  in  this  \va,j.  It  is  known  from  experiment  that  light 
passes  tlirongli  glass  or  any  other  refracting  medium  more 
slowly  than  through  a  void.  In  observations  with  a  telescope 
the  light  has  to  pass  through  the  objective,  and  the  time  lost 
in  doing  so  M-ill  make  the  aberration  appear  larger  than  it 
really  is,  and  the  velocity  of  light  will  appear  too  small.  But 
the  commonly  received  theory  (that  of  Fresnel)  is  that  this 
loss  of  time  is  compensated  by  the  objective  partially  drawing 
the  ray  with  it.  Desirous  of  setting  the  question  at  rest,  Pro- 
fessor Aiiy,  a  few  years  ago,  constructed  a  telescope,  which 
he  filled  with  water,  with  which  he  observed  the  constant  of 
aberration.  The  aberration  was  fonnd  to  be  the  same  as  with 
ordinary  telescopes,  thus  proving  the  theory  of  Fresnel  to  be 
correct,  because  on  the  other  theory  the  aberration  ought  to 
have  been  much  increased  by  the  water. 

Hence  this  explanation  of  the  difference  of  the  two  results 
fails,  and  renders  it  more  probable  that  there  is  some  error  in 
Delambre's  result.  A  reinvestigation  of  all  the  observations 
of  Jupiter's  satellites  is  very  desirable  ;  but  so  vast  is  the  labor 
that  no  one  since  Delambre  has  undertaken  it.  Mr.  Glasenapp, 
a  young  Russian  astronomer,  has,  however,  recently  investi- 
gated all  the  observations  of  Jupiter's  first  satellite  made  dur- 
ing the  years  1848-1873,  and  found  from  these  that  the  time 
required  for  light  to  pass  from  the  sun  to  the  earth  is  8  min- 
utes 20  seconds.  Instead  of  being:  smaller  than  Struve's  re- 
suit,  this  is  two  seconds  larger,  and  seven  seconds  larger  than 
that  of  Delambre.  It  is  therefore  concluded  that  the  diJ0Fer- 
ence  between  the  results  of  the  two  methods  arises  entirely 
from  the  errors  of  the  observations  used  by  Delambre,  and 
that  Struve's  time  (498  seconds)  is  not  a  second  in  error. 

Each  of  the  two  methods  we  have  described  gives  us  the 
time  required  for  light  to  pass  from  the  sun  to  the  earth ;  but 
neither  of  them  gives  us  any  direct  information  respecting  the 
velocity  of  light.  Before  we  can  deterinine  the  latter  from 
the  former,  we  must  know  what  the  distance  of  the  sun  is. 
Dividing  this  distance  in  miles  by  498,  we  shall  have  the  dis- 


THE  MOTION  OF  LIGHT.  213 

tance  which  light  travels  in  a  second.  Conversely,  if  we  can 
find  experimentally  how  far  light  travels  in  a  second,  then  by 
multiplying  this  distance  by  49S  we  shall  have  the  distance  of 
the  snn.  But  we  need  only  reflect  that  the  velocity  of  light 
is  about  180,000  miles  per  second  to  see  that  the  problem  of 
determining  it  experimentally  is  a  most  difiicult  one.  It  is 
seldom  that  objects  on  the  surface  of  the  earth  are  distinctly 
seen  at  a  greater  distance  than  forty  or  fifty  miles,  and  over 
such  a  distance  light  travels  in  the  forty-thousandth  part  of  a 
second.  As  might  be  expected,  the  earlier  attempts  to  fix  the 
time  occupied  by  light  in  passing  over  distances  so  short  as 
those  on  the  surface  of  the  earth  were  entire  failures.  The 
first  of  these  is  due  to  Galileo;  and  his  method  is  worth  men- 
tioning, to  show  the  principle  on  which  such  a  determination 
can  be  made.  He  stationed  two  observers  a  mile  or  two  apart 
by  night,  each  having  a  lantern  which  he  could  cover  in  a 
moment.  The  one  observer.  A,  M'as  to  cover  his  lantern,  and 
the  distant  one,  B,  as  soon  as  he  saw  the  light  disappeai",  cov- 
ered his  also.  In  order  that  A  might  see  the  disappearance 
of  B's  lantern,  it  was  necessary  that  the  light  should  travel 
from  A  to  B,  and  back  again.  For  instance,  if  it  took  one 
second  to  travel  between  the  two  stations,  B  would  continue 
to  see  A's  light  an  entire  second  after  it  was  really  extinguish- 
ed ;  and  if  he  then  covered  his  lantern  instantly,  A.  would 
still  see  it  during  another  second,  making  two  seconds  in  all 
after  he  had  extinguished  his  own,  besides  the  time  B  might 
have  required  to  completely  perform  the  movement  of  cover- 
ing his. 

Of  course,  by  this  rough  method  Galileo  found  no  inter- 
val whatever.  An  occurrence  which  only  requii'cd  the  hun- 
dredth part  of  the  thousandth  of  a  second  was  necessarily  in- 
stantaneous. But  we  can  readily  elaborate  liis  idea  into  the 
more  refined  methods  used  in  recent  times.  Its  essential  feat- 
ure is  that  which  must  always  be  employed  in  making  the  de- 
termination ;  that  is,  it  is  necessary  that  the  light  shall  be  sent 
from  one  station  to  another,  and  then  returned  to  the  first 
one,  where  the  double  interval  is  timed.     There  is  no  possi- 


2U 


PEACTICAL  ASTROXOMY. 


bility  of  comparing  the  times  at  two  distant  stations  witli  the 
necessary  precision.  The  first  improvement  we  sliould  make 
on  Galileo's  method  would  be  to  set  up  a  mirror  at  tlie  dis- 
tant station,  and  dispense  with  the  second  lantern,  the  ob- 
server A  seeing  his  own  lantern  by  reflection  in  the  mirror. 
Then,  if  he  screened  his  lantern,  he  would  continue  to  see  it 
by  reflection  in  the  mirror  during  the  time  the  light  required 
to  go  and  come.  But  this  also  would  be  a  total  failure,  be- 
cause the  reflection  would  seem  to  vanish  instantly.  Our  next 
effort  would  be  to  try  if  we  could  not  send  out  a  flash  of 
light  from  our  lantern,  and  screen  it  off  before  it  got  back 
again.  An  attempt  to  screen  off  a  single  flash  would  also  be 
a  failure.  "We  should  then  try  sending  a  rapid  succession  of 
flashes  through  openings  in  a  moving  screen,  and  see  wheth- 
er they  could  be  cut  off  by  the  sides  of  the  openings  before 

their  return.  This  would  be 
effected  by  the  contrivance 
shown  in  Fig.  58.  We  have 
here  a  wheel  with  spokes  ex- 
tending from  its  circumfer- 
ence, the  distance  between 
them  being  equal  to  their 
breadth.  This  wheel  is  placed 
in  front  of  the  lantern, L,  so 
tliat  the  light  from  the  latter 

Fig.  BS,-Revolving  wheel,  for  measuring  the    haS  tO  paSS  bctwecn  the  SpokeS 
velocity  of  light.  ^^f  jj^^  ^.|jggl  ^^  ^j.^^^.  ^^  ^.^^^^^ 

the  distant  mirror.  In  the  figure  the  reader  is  supposed  to  be 
between  the  wheel  and  the  reflecting  mirror,  facing  the  for- 
mer, so  that  he  sees  the  light  of  the  lantern,  and  also  the  eye 
of  the  observer,  between  the  spokes.  The  latter,  looking  be- 
tween the  spokes,  M-ill  see  the  light  of  the  lantern  reflected 
from  tlie  mirror.  Now,  suppose  he  turns  the  wheel,  still  keep- 
ing his  eye  at  the  same  point.  Then,  each  spoke  cutting  off  the 
light  of  the  lantern  as  it  passes,  there  will  be  a  succession  of 
flashes  of  light  which  will  pass  through  between  tlie  spokes, 
travel  to  the  mirror,  and  thence  be  reflected  back  again  to  the 


THE  MOTION  OF  LIGHT.  215 

wheel.  Will  they  reach  the  eye  of  the  observer  behind  the 
wheel  ?  Evidently  they  will,  if  they  return  so  quickly  that  a 
tooth  has  not  had  time  to  intervene.  But  suppose  the  wheel  to 
turn  so  rapidly  that  a  tooth  jnst  intervenes  as  the  flash  gets 
back  to  it.  Then  the  observer  will  see  no  light  in  the  mirror, 
because  each  successive  flash  is  caught  by  the  following  tooth 
just  before  it  reaches  the  observer's  eye.  Suppose,  next,  that 
he  doubles  the  speed  of  his  wheel.  Then,  while  the  flash  is 
travelHng  to  the  mirror  and  back,  the  tooth  will  have  passed 
clear  across  and  out  of  the  way  of  the  flash,  so  that  the  latter 
will  now  reach  the  observer's  eye  through  the  opening  next 
following  that  which  it  passed  through  to  leave  the  lantern. 
Thus,  the  observer  will  see  a  succession  of  flashes  so  rapid 
that  they  will  seem  entirely  continuous  to  the  eye.  If  the 
speed  of  the  wheel  be  again  increased,  the  return  flash  will  be 
caught  on  the  second  tooth,  and  the  observer  will  see  no  light, 
while  a  still  further  increase  of  velocity  will  enable  him  to 
see  the  flashes  as  they  return  through  the  second  interval  be- 
tween the  spokes,  and  so  on. 

In  pi'inciple,  this  is  Fizeau's  method  of  measuring  the  ve- 
locity of  light.  In  place  of  spokes,  he  has  exceedingly  flne 
teeth  in  a  large  wheel.  He  does  not  look  between  the  teeth 
with  the  naked  eye,  but  employs  a  telescope  so  arranged  that 
the  teeth  pass  exactly  through  its  focus.  An  arrangement  is 
made  by  which  the  light  passes  through  the  same  focus  with- 
out reaching  the  observer's  eye  except  by  reflection  from  the 
distant  mirror.  The  latter  is  placed  in  the  focus  of  a  second 
telescope,  so  that  it  can  be  easily  adjusted  to  send  the  rays 
back  in  the  exact  direction  from  which  they  come.  To  find 
the  time  it  takes  the  light  to  travel,  it  is  necessaiy  to  know  the 
exact  velocity  of  the  wheel  which  will  cut  off  the  retui'n  light 
entirely,  and  thence  the  number  of  teeth  which  ]>a?s  in  a  sec- 
ond. Suppose,  for  instance,  that  the  Avheel  had  a  thousand 
teeth,  and  the  reflector  was  nine  miles  away,  so  that  the  light 
had  to  travel  eighteen  miles  to  get  back  to  the  focus  of  the 
telescope.  Then  it  would  be  found  that  with  a  velocity  of 
about  five  turns  of  the  wheel  per  second,  the  light  would  be 


216  PBACTICAL  ASTEOXOMY. 

tirat  cut  off.  Increasing  the  velocity,  it  would  reappear,  and 
would  grow  brighter  until  the  velocity  reached  ten  turns  per 
second.  It  would  then  begin  to  fade  away,  and  at  fifteen 
turns  per  second  would  be  again  occulted,  and  so  on.  With 
the  latter  velocity,  fifteen  thousand  teeth  and  fifteen  thousand 
intervals  would  pass  in  a  second,  while  two  teeth  and  one  in- 
terval passed  during  the  time  the  light  was  performing  its 
journey.  The  latter  would,  therefore,  be  performed  in  the 
ten-thousandth  part  of  a  second,  showing  the  actual  velocity 
to  be  180,000  miles  per  second.  The  most  recent  determina- 
tion made  in  this  way  is  l)y  M.  Coi'uu,  of  Paris,  who  has  made 
some  improvements  in  the  mode  of  applying  it.  His  results 
will  be  described  presently. 

Ingenious  and  beautiful  as  this  method  is,  I  do  not  think  it 
can  be  so  accurate  as  another  employed  by  Foucault,  in  which 
it  is  not  a  toothed  wheel  which  revolves,  but  a  Wheatstone 
mirror.    To  explain  the  details  of  the  apparatus  actually  used 

would    be    tedious, 
^_g  but  the  principle  on 

which  the  method 
rests  can  be  seen 
quite  readily.  Sup- 
pose AB,  Fig.  59,  to 
represent  a  flat  mir- 
ror, seen  edgewise, 
revolving  round  an 
r^/'  axis  at  X,  and  C  a 

Fio.  59— Illustratiug  FoucauU's  method  of  measuring  the    fixcd    COncave    miF- 

veiocity  of  light.  ^.^^.^  g^  Y>^Rced  that 

the  centre  of  its  concavity  shall  fall  on  JC.  Let  0  be  a  lumi- 
nous point,  from  which  emanates  a  single  ray  of  light,  OX. 
This  ray,  meeting  the  mirror  at  A',  is  reflected  to  the  concave 
mirror,  C.  which  it  meets  at  a  right  angle,  and  is  therefore  re- 
flected directly  back  on  the  line  from  which  it  came,  first  to 
X,  and  then  through  the  point  0,  from  which  it  emanated,  so 
that  an  eye  stationed  at  £"  will  see  it  returning  exactly  tlirough 
tlie  point  0.     Xo  matter  how  the  observer  may  turn  the  mir* 


THE  MOTION  OF  LIGHT.  217 

ror  AB,  he  cannot  make  the  reflected  ray  deviate  from  this 
line:  he  can  only  make  it  strike  a  different  point  of  the  mir- 
ror C.  If  he  turns  AB  so  that  after  the  ray  is  reflected  froiii 
it,  it  does  not  strike  C  at  all,  then  he  will  see  no  return  ray. 
If  the  ray  is  reflected  back  at  all,  it  will  pass  through  0.  This 
result  is  founded  on  the  supposition  that  the  mirror  AB  re- 
mains in  the  same  position  during  the  time  the  ray  occupies 
in  passing  from  X  to  C  and  back.  But  suppose  the  mirror 
AB  to  be  revolving  so  rapidly  that  when  the  ray  gets  back 
to  X,  the  mirror  has  moved  to  the  position  of  the  dotted  line 
A'B'.  Then  it  will  no  longer  be  reflected  back  through  0, 
but  will  be  sent  in  the  direction  E',  the  angle  EXE'  being 
double  that  through  which  the  mirror  has  moved  during  the 
time  the  ray  was  on  its  passage.  Knowing  the  velocity  of 
the  mirror,  and  the  angle  EXE',  this  time  is  easily  found. 

Evidently  the  observer  cannot  see  a  continuous  light  at  E\ 
because  a  reflection  can  be  sent  back  only  when  the  revolving 
mirror  is  in  such  a  position  as  to  send  the  ray  to  some  point 
of  the  concave  mirror,  C.  What  will  really  be  seen,  therefore, 
is  a  succession  of  flashes,  each  flash  appearing  as  the  revolving 
mirror  is  passing  through  the  position  AB.  But  when  the 
mirror  revolves  rapidly,  these  flashes  will  seem  to  the  eye  to 
form  a  continuous  light,  which,  however,  will  be  fainter  than 
if  the  mirror  were  at  rest,  in  the  proportion  which  the  arc  of 
the  concave  mirror,  C,  bears  to  an  entire  circle.  Beyond  the 
enfeeblement  of  the  light,  this  want  of  continuity  is  not  pro- 
ductive of  any  inconvenience.  It  was  thus  found  by  Fou- 
cault  that  the  velocity  of  light  was  185,000  miles  per  second,  a 
result  which  is  probably  within  a  thousand  miles  of  the  truth. 

The  preceding  explanation  shows  the  principle  of  the  meth- 
od, but  not  the  details  necessary  in  applying  it.  It  is  not 
practicable  to  isolate  a  single  ray  of  light  in  the  manner  sup 
posed  in  the  figure,  and  therefore,  without  other  apparatus, 
the  light  from  0  would  be  spread  all  over  the  space  around  E 
and  E'.  The  desired  result  is  obtained  by  placing  a  lens  be- 
tween the  luminous  point  0  and  the  revolving  mirror  in  such 
a  position  that  all  the  light  falling  from  0  upon  the  lens  shall, 


218  PRACTICAL  ASTEOXOMY. 

after  reflection,  be  brought  to  a  focus  upon  the  surface  of  the 
conca%e  mirror,  C.  Then  when  tlie  mirror  AB  is  made  to  re- 
volve rapidly,  the  return  rays  passing  back  through  the  lens 
on  their  return  journey  are  brought  to  a  focus  at  a  point 
along-side  0,  and  distant  from  it  by  an  amount  which  is  pro- 
portional to  the  time  the  light  has  required  to  pass  from  X  to 
Cand  back  again. 

So  delicate  is  this  method,  that  the  millionth  of  a  second  of 
time  can  be  measured  by  it  as  accurately  as  a  carpenter  can 
measure  the  breadth  of  a  board  with  his  rule.  Its  perfection 
is  the  result  of  the  combined  genius  of  several  men.  The  lirst 
idea  of  employing  a  revolving  mirror  in  the  measurement  of 
a  very  minute  interval  of  time  is  due  to  the  late  Sir  Charles 
Wheatstone,  who  thus  measured  the  duration  of  the  electric 
spark.  Then  Arago  showed  that  it  could  be  applied  to  de- 
termine whether  the  velocity  of  light  was  greater  in  water 
or  in  air.  Fizeau  and  Foucault  improved  on  Arago's  ideas 
by  the  introduction  of  the  concave  mirror,  having  its  centre 
of  curvature  in  the  revolving  mirror,  and  then  this  wondei-f  nl 
piece  of  apparatus  was  substantially  complete.  The  last  de- 
termination of  the  velocity  of  light  with  it  was  made  by  Fou- 
cault, and  communicated  to  the  French  Academy  of  Sciences 
in  1862,  with  the  statement  tiiat  the  velocity  resulting  from 
all  his  experiments  was  298,000  kilometres  (185,200  miles) 
per  second. 

The  problem  in  question  was  next  taken  up  by  Cornu,  of 
Paris,  whose  result  has  already  been  alluded  to.  Notwith- 
standing the  supposed  advantages  of  the  Foucault -Wheat- 
stone  method,  M.  Cornu  preferred  that  of  Fizeau.  His  first 
results,  reached  in  1872,  accorded  quite  well  with  those  of 
Foucault  just  cited,  indicating  a  small  but  somewhat  uncer- 
tain increase.  His  experiments  were  repeated  in  1874,  and 
their  results  were  communicated  to  the  French  Academy  of 
Sciences  in  December  of  that  year.  In  this  last  series  of 
measurements  his  station  was  the  observatory,  and  the  distant 
mirror  was  placed  on  the  tower  of  Montlhery,  at  a  distance  of 
about  fouiixjen  English  miles.     The  telescope  through  which 


THE  MOTION  OF  LIGHT.  219 

the  flashes  of  light  were  sent  and  received  was  twenty-nine 
feet  long  and  of  fourteen  inches  aperture.  The  velocity  of 
the  toothed  wheel  could  be  made  to  exceed  1600  turns  a  sec- 
ond, and  by  the  electro-chronograph,  on  which  the  revolutions 
w^ere  recorded,  the  time  could  be  determined  within  the  thou- 
sandth of  a  second.  At  Montlhery,  the  telescope,  in  the  focus 
of  which  the  reflecting  mirror  was  placed,  was  six  inches  in 
aperture,  and  was  held  by  a  large  cast-iron  tube  set  in  the 
masonry  of  the  tower.  At  this  distance  M.  Cornu  was  able, 
with  the  highest  velocity  of  his  revolving  wheel,  to  make 
twenty  of  its  teeth  pass  before  the  flashes  of  light  got  back, 
and  to  catch  them,  on  their  return,  on  the  twenty-first  tooth. 
His  conclusion  was  a  velocity  of  300,400  kilometres  per  sec- 
ond in  air,  or  300,330  in  a  vacuum. 

The  toothed  wheel  is  a  very  uncertain  measuring  instru- 
ment, in  comparison  with  the  revolving  mirror  just  described. 
It  received  tlie  preference  because,  on  Foucault's  plan,  the 
measures  had  to  be  made  within  the  compass  of  a  single  room, 
while  with  the  toothed  wheel  the  light  could  travel  fourteen 
miles  and  back.  What  was  wanted  was  a  modification  of  the 
revolving  mirror,  so  that  the  return  flash  could  be  seen  from  a 
great  distance.  Tliis  was  effected  during  the  years  1878-82 
by  Professor  A.  \.  Michelson  and  the  writer.  In  their  final 
experiments  the  revolving  mirror  was  fixed  at  a  station  in  the 
grounds  of  Fort  Myer,  near  Washington,  and  the  light  was  re- 
flected from  a  fixed  mirror  at  the  base  of  the  Washington 
Monument,  on  the  other  side  of  the  Potomac,  two  miles  and  a 
quarter  away.  The  time  required  for  tlie  light  to  go  and  come 
was  found  to  be  less  than  ^^^q^^  of  a  second.  If  tlio  measure 
of  so  minute  an  interval  seems  incredible,  we  must  consider 
that  a  mirror  revolving  250  times  a  second  will  turn  through 
^i°  i'^  4000D  o^  ^  second,  and  this  angle  is  easily  measured. 
The  resulting  velocity  was  299,860  kiloi^.ietres  per  second,  with 
an  uncertainty  of  less  than  100.  At  this  rate  light  would  make 
the  circuit  of  the  eaith  seven  and  a  half  times  in  a  second. 


220  PRACTICAL  ASTRONOMY. 


CHAPTER  y. 

THE     SPECTROSCOPE. 

In  one  of  Dr.  Lardner's  popular  lectures  on  astronomy,  de- 
livered some  thirty  years  ago,  lie  introduced  the  subject  of 
weighing  the  planets  as  one  in  which  he  could  with  difficulty 
expect  his  statements  to  be  received  with  credulity.  That 
men  should  measure  the  distances  of  the  planets  was  a  state- 
ment he  expected  his  hearers  to  receive  with  surprise ;  but  the 
step  from  measui'ing  to  weighing  was  so  long  a  one,  that  it 
seemed  to  the  ordinary  mind  to  extend  beyond  all  the  bounds 
of  possibility. 

Had  a  hearer  told  the  lecturer  that  men  would  also  be  able 
to  determine  the  chemical  constituents  of  the  sun  and  stai*s, 
and  to  tell  whether  any  of  them  did  or  did  not  contain  iron, 
hydrogen,  and  other  chemical  elements,  the  lecturer  would 
probably  have  replied  that  that  statement  quite  exceeded  the 
limits  of  his  own  credulity ;  that,  while  he  himself  saw  clearl}' 
how  the  planets  were  measured  and  weighed,  he  looked  upon 
the  idea  of  determining  their  chemical  con'^fitution  as  a  mere 
piece  of  pleasantry,  or  the  play  of  an  exuberant  fancy.  And 
yet,  this  very  thing  has,  to  a  certain  extent,  been  done  by  the 
aid  of  the  spectroscope.  The  chemical  constitution  of  matter 
in  the  state  of  gas  or  vapor  can  be  detected  almost  as  readily 
at  the  distance  of  the  stars  as  if  we  had  it  in  our  laboratories. 
The  difficulties  which  stand  in  the  way  do  not  arise  from  the 
distance,  but  from  the  fact  that  matter  in  the  heavenly  bodies 
seems  to  exist  in  some  state  which  we  have  not  succeeded  in 
exactly  reproducing  in  our  laboratories.  Like  many  other 
wonders,  spectrum  analysis,  as  it  is  called,  is  not  at  all  extraor- 
dinary after  we  see  how  it  is  done.     Indeed,  the  only  wonder 


TEE  SPECTROSCOPE.  221 

now  is  how  the  first  half  of  this  century  could  have  passed 
without  physicists  discovering  it.  The  essential  features  of 
the  method  are  so  simple  that  only  a  knowledge  of  the  ele- 
ments of  natural  philosophy  is  necessary  to  enable  them  to  be 
understood.     We  shall,  therefore,  briefly  explain  them. 

It  is  familiarly  known  that  if  we  pass  the  rays  of  the  sun 
which  enter  a  room  by  a  small  opening  through  a  prism,  the 
light  is  separated  into  a  number  of  bright  colors,  which  are 
spread  out  on  a  certain  scale,  the  one  end  being  red  and  the 
other  violet,  while  a  long  range  of  intermediate  colors  is  found 
between  them.  This  shows  that  common  white  liglit  is  really 
a  compound  of  every  color  of  the  spectrum.  This  compound 
is  not  like  chemical  compounds,  made  up  of  two  or  three  or 
some  limited  number  of  simples,  but  is  composed  of  an  infini- 
ty of  different  kinds  of  light,  all  running  into  eacli  other  by 
insensible  degrees ;  the  difference,  however,  being  only  in  col- 
or, or  in  the  capacity  of  being  refracted  by  the  prism  througli 
which  it  passes.  This  arrangement  of  colors,  spread  out  to  our 
siglit  according  to  the  refrangibility  of  the  light  which  forms 
them,  is  called  the  spectrum.  By  the  spectrum  of  any  object 
is  meant  the  combination  of  colors  found  in  the  light  wliicli 
emanates  from  that  object.  For  instance,  if  we  pass  tlie  light 
from  a  candle  through  a  prism,  so  as  to  separate  it  into  its 
component  colors,  and  make  the  light  thus  separated  fall  on 
a  screen,  the  arrangement  of  colors  on  the  screen  would  be 
called  the  spectrum  of  the  candle.  If  we  look  at  a  bright 
star  through  a  prism,  the  combination  of  colors  which  we  see 
is  called  the  spectrum  of  the  star,  and  so  with  any  other  object 
we  may  choose  to  examine. 

As  the  experiment  of  forming  a  spectrum  is  commonly 
made,  there  is  a  slight  mixing-up  of  light  of  the  different  col- 
ors, because  light  of  the  same  degree  of  refrangibility  will 
fall  on  different  parts  of  the  screen  according  to  tlie  part  of 
the  prism  it  passes  through.  When  the  separation  of  the  liglit 
is  thus  incomplete,  the  spectrum  is  said  to  be  impure.  In  or- 
der to  make  any'  successful  examination  of  the  light  which 
emanates  from  an  object,  our  spectrum  must  be  pure ;  that  is, 


222  PRACTICAL  ASTRONOMY. 

each  point  of  the  spectrum  must  be  formed  by  light  of  one 
degree  of  refraugibility.  To  effect  this  in  the  most  perfect 
^vaJ,  the  spectrum  is  not  formed  on  a  screen,  but  on  the  retina 
of  the  observer's  eye.  An  instrument  by  which  this  is  done 
is  called  a  spectroscope. 

The  most  essential  parts  of  a  spectroscope  consist  of  a  small 
telescope  with  a  prism  in  front  of  the  object-glass.  The  ob- 
server must  adjust  his  telescope  so  that,  removing  the  prism, 
and  looking  directly  at  the  object,  he  shall  obtain  distinct  vis- 
ion of  it.  Then,  putting  the  prism  in  its  place,  and  turning 
the  telescope  to  snch  an  angle  that  the  light  which  comes  from 
the  object  shall,  after  being  I'efracted  by  the  prism,  pass  direct- 
ly into  the  telescope,  he  looks  into  the  latter.  When  the  prop- 
er adjustments  are  made,  he  will  see  a  pure  spectrum  of  the 
object.  In  order  that  this  experiment  may  succeed,  it  is  es- 
sential that  the  object,  when  viewed  directly,  shall  present  the 
appearance  of  a  point,  like  a  star  or  planet.  If  it  is  an  object 
which  has  a  measurable  surface,  like  the  sun  or  moon,  he  will 
see  either  no  spectrum  at  all  or  only  a  very  impure  one. 

For  this  reason,  a  spectroscope  which  consists  of  nothing  but 
a  telescope  and  prism  is  not  fitted  for  any  purpose  but  that  of 
trial  and  illustration.  To  fit  it  for  general  use,  another  ob- 
ject-glass, with  a  slit  in  its  focus,  is  added.     Fig.  60  shows  the 


Fig.  60.— Coarse  of  rays  through  a  spectroscope. 

essential  parts  of  a  modern  spectroscope.  At  the  farther  end 
of  the  second  telescope,  where  the  light  enters,  is  a  narrow 
slit,  which  can  be  opened  or  closed  by  means  of  a  screw,  and 


THE  SPECTROSCOPE.  223 

through  which  the  light  fi-om  the  object  is  admitted.  The 
rays  of  light  following  the  dotted  lines  are  made  parallci  by 
passing  tlirongh  the  lens,  Z.  They  then  fall  on  the  prisnjjP, 
by  which  they  are  refracted,  and  from  which  they  emerge  par- 
allel, except  that  the  direction  of  the  rays  of  different  colors 
is  different,  owing  to  the  greater  or  less  degree  of  refi-action 
produced  by  the  prism.  They  then  pass  through  the  ol)ject- 
glass  of  the  telescope,  T,  by  which  the  rays  of  each  color  are 
brought  to  a  focus  at  a  particular  point  in  the  field  of  view, 
the  red  rays  all  coming  togetlier  at  the  lower  point,  the  violet 
ones  at  the  upper  point,  and  those  of  each  intermediate  color 
at  tlieii"  proper  place  along  the  line.  The  observer,  looking 
into  tlie  telescope,  sees  the  spectrum  of  whatever  object  is 
throwiuij;-  its  lio;ht  through  the  slit. 

If  the  object  of  which  the  observer  wishes  to  see  the  speo 
trum  is  a  flame,  he  places  it  immediately  in  front  of  the  slit; 
and  if  it  is  an  object  of  sensible  surface,  like  the  sun  or  moon, 
he  points  the  collimator,  C,  directly  at  it,  so  that  the  light 
which  enters  the  slit  shall  fall  on  the  lens,  Z.  But  if  it  is  a 
star,  he  cannot  get  light*  enough  in  this  way  to  see  it,  and  he 
must  either  i-emove  his  collimator  entirelj',  or  fasten  his  spec- 
troscope to  the  end  of  a  telescope,  so  that  the  slit  shall  be 
exactly  in  the  focus.  The  latter  is  the  method  universally 
adopted  in  examining  the  spectrum  of  a  star. 

If,  with  this  instrument,  we  examine  the  light  which  comes 
from  a  candle,  from  the  Are,  or  from  a  piece  of  white-hot 
iron,  we  shall  find  it  to  be  continuous ;  that  is,  there  is  no  gap 
iu  the  series  of  colors  from  one  end  to  the  other.  But  if  we 
take  the  light  from  the  sun,  or  from  the  moon,  a  planet,  or 
any  object  illuminated  by  the  sun,  we  shall  find  the  spectrum 
to  be  crossed  by  a  great  number  of  fine  dark  lines,  showing 
that  certain  kinds  of  light  are  wanting.  It  is  now  known 
that  tlie  particular  kinds  of  light  which  originally  belonged 
in  these  dark  lines  have  been  culled  out  by  the  gases  surround- 
ing the  sun  through  which  the  light  has  passed.  This  culling- 
out  is  called  Selective  Absorption.  It  is  found  by  experiment 
that  each  kind  of  gas  has  its  own  liking  for  light  of  peculiar 
L  16 


224:  PRACTICAL  ASTROyOMY. 

degrees  of  refrangibility,  and  absorbs  the  light  which  belongs 
in  the  corresponding  parts  of  the  spectrum,  letting  all  the 
other  light  pass. 

Perhaps  we  may  illustrate  this  process  by  a  similar  one 
which  Me  might  imagine  mankind  to  perform.  Suppose  Nat- 
ure should  loan  us  an  immense  collection  of  many  millions 
of  gold  pieces,  out  of  which  we  were  to  select  those  M-hich 
would  serve  ns  for  money,  and  return  her  the  remainder. 
The  English  rummage  through  the  pile,  and  pick  out  all  the 
pieces  which  are  of  the  proper  weight  for  sovereigns  and  half- 
sovereigns  ;  the  French  pick  out  those  which  will  make  live, 
ten,  twenty,  or  fifty  franc  pieces ;  the  Americans  the  one,  five, 
ten,  and  twenty  dollar  pieces,  and  so  on.  After  all  the  suit- 
able pieces  are  thus  selected,  let  the  remaining  mass  be  spread 
out  on  the  ground  accoi'ding  to  the  respective  weights  of  the 
pieces,  the  smallest  pieces  being  placed  in  a  row,  the  next  in 
weight  in  an  adjoining  row,  and  so  on.  We  shall  then  find  a 
number  of  rows  missing :  one  which  the  French  have  taken 
out  for  five-franc  pieces;  close  to  it  another  which  the  Amer- 
icans have  taken  for  dollars;  afterwards  a  row  which  have 
gone  for  half-sovereigns,  and  so  on.  By  thus  arranging  the 
pieces,  one  would  be  able  to  tell  what  nations  had  culled  over 
the  pile,  if  he  only  knew  of  what  weight  each  one  made  its 
coins.  The  gaps  in  the  places  where  the  sovereigns  and  half- 
sovereigns  belonged  would  indicate  the  English,  that  in  the 
dollars  and  eagles  the  Americans,  and  so  on.  If,  now,  we  re- 
flect how  utterly  hopeless  it  would  appear,  from  the  mere  ex- 
amination of  the  miscellaneous  pile  of  pieces  which  had  been 
left,  to  ascertain  what  people  had  been  selecting  coins  from  it, 
and  how  easy  the  problem  would  appear  when  once  some 
genius  should  make  the  proposed  arrangement  of  the  pieces 
in  rows,  we  shall  see  in  what  the  fundamental  idea  of  spec- 
tmm  analysis  consists.  The  formation  of  tlie  spectrum  is  the 
separation  and  arrangement  of  the  light  which  comes  from  an 
object  on  the  same  system  by  which  we  have  supposed  the 
gold  pieces  to  be  arranged.  The  gaps  we  see  in  the  specti'um 
tell  the  tale  of  the  atmosphere  through  which  the  light  has 


THE  SPECTROSCOPE.  225 

passed,  as  in  the  case  of  the  coins  they  would  tell  what  nations 
had  sorted  over  the  pile. 

That  the  dark  lines  in  the  solar  spectrum  are  picked  out  by 
the  gases  of  the  sun's  atmosphere  has  long  been  surmised ;  in- 
deed, Sir  John  Ilerschel  seems  to  have  had  a  clear  idea  of 
the  possibility  of  spectrum  analysis  half  a  century  ago.  The 
difficulty  was  to  find  what  particular  lines  any  particular  sub- 
stance selects ;  since,  to  exert  any  selective  action,  a  vastly 
greater  thickness  of  gas  is  generally  i-equired  than  it  is  prac- 
ticable to  obtain  experimentally.  This  difficulty  was  sur- 
mounted by  the  capital  discovery  of  Kirchhoff  and  I3unsen, 
that  a  gloiuing  gas  gives  out  rays  of  the  same  degree  of  refranglhil- 
ity  which  it  absorbs  when  light  passes  through  it.  For  example, 
if  we  put  some  salt  into  the  flame  of  a  spirit-lamp,  and  ex- 
amine the  spectrum  of  the  light,  we  shall  find  a  pair  of  bright- 
yellow  lines,  which  correspond  most  accurately  to  a  pair  of 
black  lines  in  the  solar  spectrum.  These  lines  are  known  to 
be  due  to  sodium,  a  component  of  common  salt,  and  their  ex- 
istence in  the  solar  spectrum  shows  that  there  is  sodium 
in  the  sun's  atmosphere.  They  are  therefore  called  the  sodi- 
um lines.  By  vaporizing  various  substances  in  sufficiently  hot 
flames,  the  spectra  of  a  great  number  of  metals  and  gases 
have  been  found.  Sometimes  there  are  only  one  or  two  bright 
lines,  while  with  iron  the  number  is  counted  by  hundreds. 
The  quantity  of  a  substance  necessary  to  form  these  bright 
lines  is  so  minute  that  tlie  presence  of  some  metals  in  a  com- 
pound have  been  detected  with  tlie  spectroscope  when  it  was 
impossible  to  find  a  trace  of  them  in  any  other  way.  Indeed, 
two  or  three  new  metals,  the  existence  of  which  was  before  en- 
tirely unknown,  first  told  their  story  through  the  spectroscope. 

The  general  relations  of  the  spectrum  to  the  state  of  the 
substance  from  wliicli  the  light  emanated  may  be  condensed 
into  three  rules,  or  laws,  as  follows : 

1.  The  light  from  a  glowing  solid,  liquid,  or  non-transparent 
gas  forms  a  continuous  spectrum,  in  which  neither  bright  nor 
dark  lines  are  found.  The  spectrum  is  of  the  same  nature,  no 
matter  how  finely  the  substance  may  be  divided. 


226  PRACTICAL  ASTRONOMY. 

2.  If  the  light  from  the  glowing  solid  passes  through  a  gas- 
eous atmosphere,  the  spectrum  will  be  crossed  by  dark  lines 
occupying  those  parts  of  the  spectrum  where  the  light  culled 
out  by  the  atmosphere  belongs. 

3.  A  glowing  gas  sends  out  light  of  the  same  degrees  of 
refrangibility  as  belong  to  that  which  it  absorbs,  so  that  its 
spectrum  consists  of  a  system  of  bright  lines  occupying  the 
same  position  as  the  dark  lines  it  would  produce  by  absoi-ption. 

If,  then,  on  examining  the  spectrum  of  a  star  or  other  heav- 
enly body,  we  find  only  bright  lines  with  dark  spaces  between 
them,  we  may  conclude  that  the  body  consists  of  a  glowing 
gas,  and  we  judge  w^hat  the  gas  is  by  comparing  the  spectrum 
with  those  of  various  substances  on  the  earth.  If,  on  the  oth- 
er hand,  the  spectrum  is  a  continuous  one,  except  where  cross- 
ed b}'  fine  dark  lines,  we  conclude  that  it  emanates  from  a 
glowing  body  surrounded  by  an  atmosphere  which  culls  out 
some  of  the  rays  of  light. 

It  will  be  seen  that  the  spectroscope  gives  us  no  definite  in- 
formation respecting  the  nature  or  composition  of  bodies  in 
the  solid  state.  If  we  heat  any  sort  of  metal  white-hot,  sup- 
posing only  that  it  will  stand  this  heat  without  being  vapor- 
ized, we  shall  have  a  spectrum  continuous  from  end  to  end,  in 
which  there  will  be  neither  bright  nor  dark  lines  to  give  any 
indications  respecting  the  substance.  In  order,  therefore,  to 
detect  the  presence  of  any  chemical  element  with  this  instru- 
ment, that  element  must  be  in  the  form  of  gas  or  vapor.  Here 
■we  have  one  limitation  to  the  application  of  the  spectroscope 
to  the  celestial  bodies.  The  tendency  of  bodies  in  space  is  to 
cool  off,  and  when  they  have  once  become  so  cool  as  to  solidi- 
fy, the  instrument  in  question  can  give  us  no  further  definite 
information  respecting  their  constitution. 

Even  if  the  body  be  in  the  gaseous  state,  we  cannot  always 
rely  on  the  spectroscope  informing  us  with  certainty  of  the 
nature  of  the  gas.  The  light  we  analyze  must  either  be  emit- 
ted by  the  gas,  the  latter  being  so  hot  as  to  shine  by  its  own 
light,  or  it  must  be  transmitted  through  it.  Thus,  the  appli- 
cation of  spectrum  analysis  is  confined  to  glowing  gases  and 


THE  SPECTROSCOPE.  227 

the  atmospheres  of  the  stars  and  planets,  the  application  to  the 
latter  depending  on  the  fact  that  the  sunlight  reflected  from 
the  surface  of  the  planet  passes  twice  through  its  atmosphere. 
Even  in  these  cases  the  intei-pretation  of  its  results  is  sometimes 
rendered  difficult  in  consequence  of  the  varied  spectrum  of  the 
same  gas  at  different  temperatures  and  under  different  degrees 
of  pressure.  Under  some  conditions  so  many  new  lines  are 
introduced  into  the  spectrum  of  hydrogen  that  it  can  hardly 
be  recognized.  As  a  general  rule,  the  greater  the  pressure,  the 
greater  the  number  of  lines  which  appear ;  indeed,  it  has  been 
found  by  Lockyer  and  Frankland  that  as  the  pressure  and  den- 
sity of  a  gas  are  increased,  its  spectrum  tends  to  become  con- 
tinuous. We  must  therefore  regard  the  third  of  the  above 
rules  respecting  spectrum  analysis,  or,  rather,  the  general  rule 
that  a  glowing  gas  gives  a  spectrum  of  bright  lines,  as  not  uni- 
versally true.  If  we  could,  by  artificially  varying  the  temper- 
ature, pressure,  and  composition  of  gases,  accurately  reproduce 
the  spectrum  of  a  celestial  body,  the  changes  of  tlie  spectrum 
which  we  have  mentioned  would  be  a  positive  advantage ; 
since  they  would  enable  us  to  determine,  not  merely  the  com- 
position of  a  gaseous  body,  but  its  temperature  and  pressure. 
This  is,  however,  a  field  in  wliich  success  has  iiot  yet  been 
reached. 

There  is  still  another  circumstance  which  renders  the  speC' 
tra  of  the  heavenly  bodies  more  complex  than  was  at  first  sup- 
posed, but  which  may,  by  this  very  complexity,  enable  us  to 
make  great  advances  in  our  knowledge  of  the  physical  consti- 
tution of  the  sun  and  stars.  It  is  that  the  two  classes  of  spec- 
tra just  described — namely,  (1)  a  continuous  spectrum  crossed 
by  dark  lines,  and  (2)  a  spectrum  composed  wholly  of  bright 
lines — ^are  only  two  extreme  cases,  and  that  in  many  cases 
they  are  combined  in  very  different  proportions.  If  a  white- 
hot  body  is  composed  of  a  glowing  atmosphere,  the  hotter 
substances  of  this  atmosphere  may  show  bright  lines,  while 
the  cooler  substances  may  absorb  dark  lines  from  the  light 
emitted  by  the  hot  body  below.  Thus,  we  may  have  bright 
lines,  dark  lines,  and  strips  of  continuous  spectrum  all  mixed 


228  PEACTICAL  ASTROXOMY. 

up  in  such  a  way  that  it  may  be  bard  to  interpret  what  is 
seen.  Tlie  difficulty  is  to  know  wbetber  a  narrow,  dark  space 
is  produced  by  the  absorption  of  a  gas,  or  M'hether  it  is  simply 
an  interval  between  two  bright  gaseous  lines ;  and  whether  a 
narrow,  bright  space  is  produced  by  a  glowing  gas,  or  whether 
it  is  a  small  strip  of  continuous  spectrum  from  a  glowing  solid 
between  two  absorption  bands.  We  have  a  mixed-up  spec- 
trum of  this  kind  in  the  Bessemer  furnace.  The  difficulty  is 
increased  by  the  fact  that  the  dark  portions  culled  out  by  the 
absorption  of  the  cooler  gases  are  not  always  fine  perfectly 
dark  lines,  but  in  many  cases  are  broad,  grayish  bands.  It  is, 
indeed,  possible  that  these  bands  may  be  made  up  of  groups 
of  fine  lines,  too  close  to  be  separately  seen ;  but  so  long  as  the 
separate  lines  cannot  be  distinguished,  this  question  must  be 
undecided. 

Until  very  lately,  it  was  always  supposed  that  the  spectrum 
of  the  light  of  the  sun,  so  far  as  it  could  be  analyzed,  was 
continuous  from  end  to  end,  except  where  dark  absorption 
lines  crossed  it.  A  remarkable  addition  to  this  theory  has, 
however,  been  made  by  Professor  Henry  Draper,  of  New 
York,  the  main  point  of  the  addition  being  that  the  spectrum 
is  crossed  by  the  bright  lines  and  bands  arising  from  glowing 
gases,  and  that  these  lines  admit  of  being  recognized  in  cer- 
tain parts  of  the  spectrum  if  the  proper  steps  are  taken  to 
bring  them  out.  That  bright  lines  might  well  exist  in  the 
spectrum  no  one  would  deny,  because  the  gases  of  the  clii-o- 
mosphere  must  produce  them.  But  Mr.  Lockyer  was  the  only 
investigator  who  had  attempted  to  show  that  such  lines  could 
really  be  seen,  and  his  observations  had  been  very  generally 
overlooked.  Dr.  Drapers  course  was  to  photograph  side  by 
side  the  solar  spectrum  between  the  lines  G  and  H,  and  the 
corresponding  part  of  the  spectrum  of  oxygen  rendered  lumi- 
nous by  the  electric  spark.  The  result  is  that  out  of  thirteen 
bright  lines  of  oxygen,  some  of  them  double  or  treble,  nearly 
all  have  corresponding  lines  in  the  solar  spectrum.  The  co- 
incidence is  so  striking  that  it  seems  hardly  possible  to  avoid 
the  conclusion  that  a  considerable  part  of  the  violet  light  of 


THE  SPECTROSCOPE.  229 

the  son's  spectrum  arises  from  glowing  oxygen  in  the  plioto- 
sphere.  But  the  best  authorities  still  differ  as  to  the  inter- 
pretation to  be  put  upon  these  coincidences. 

What  gives  especial  interest  to  this  investigation  by  Jjr. 
Draper  is  that  it  affords  the  first  evidence  which  science  has 
found  of  the  existence  of  oxygen  in  the  sun,  the  dark  lines 
which  would  be  produced  by  that  substance  having  been 
looked  for  in  vain.  It  would  seem  either  that  the  capacity  ot 
oxygen  for  absorbing  light  selectively  is  very  small,  or  that  it 
exists  in  the  sun  only  at  a  very  high  temperature. 

The  reason  why  tiiese  lines  are  brought  out  here  when  they 
are  not  found  in  other  parts  of  tlie  spectrum  is  to  be  found 
in  the  extreme  faintness  of  the  violet  part  of  the  continuous 
spectrum,  whereby  the  bright  lines  are  not  obscured  by  the 
dazzling  brilliancy  of  the  background  of  continuous  spectrum. 
If  it  be  asked  why  these  bright  lines  have  not  been  noticed 
before,  the  answer  is,  that  the  dark  lines  are  here  so  broad 
and  numerous  as  to  cut  up  the  continuous  spectrum  into  very 
narrow  lines  of  very  irregular  bi'ightness,  besides  which  ab- 
sorption bands  or  half  shades  are  numerous.  Again,  the  lines 
of  oxygen  do  not  appear  to  be  so  narrow  and  6har[)ly  defined 
as  those  of  the  metallic  vapors,  and  this  makes  it  more  difii 
cult  to  distinguish  them  from  spaces  between  the  dark  bands. 

The  reader  now  understands  that  when  the  light  from  a  ce- 
lestial object  is  analyzed  by  the  prism,  and  the  component  col- 
ors are  spread  out  singly  as  on  a  sheet,  the  dark  and  bright 
lines  which  we  see  are  the  letters  of  the  open  book  which  we 
are  to  interpret  so  as  to  learn  w^hat  they  tell  us  of  the  body 
from  which  the  light  came,  or  the  vapors  through  which  it 
passed.  When  we  see  a  line  or  a  set  of  lines  w^hich  we  rec- 
ognize as  produced  by  a  known  substance,  we  infer  the  pres- 
ence of  that  substance.  The  question  may  now  be  asked,  ITow 
do  we  know  but  that  tlie  lines  we  observe  may  be  produced 
by  other  substances  besides  those  wdiich  we  find  to  produce 
them  in  our  laboratories  ?  May  not  the  same  lines  be  pro- 
duced by  different  substances  ?  This  question  can  be  an- 
swered only  by  an  appeal  to  probabilities.     The  evidence  in 


230  PltACTICAL  ASTRONOMY. 

the  case  is  much  the  same  as  that  by  wliich,  recognizing  the 
picture  of  a  friend,  we  conchide  that  it  is  not  the  picture  of 
any  one  else.  For  anything  we  can  prove  to  the  contrary, 
another  person  might  have  exactly  the  same  features,  and 
might,  therefore,  make  the  very  same  picture.  But,  as  a  mat- 
ter of  fact,  we  know  that  practically  no  two  men  whom  we 
have  ever  seen  do  look  exactly  alike,  and  it  is  extremely  im- 
probable that  they  ever  would  look  so.  The  case  is  the  same 
in  spectrum  analysis.  Among  the  great  number  of  substances 
which  have  been  examined  with  the  spectroscope,  no  two  give 
the  same  lines.  It  is  therefore  extremely  improbable  that  a 
given  system  of  bright  lines  could  be  produced  by  more  than 
one  substance.  At  the  same  time,  the  evidence  of  the  spec- 
troscope is  not  necessarily  conclusive  in  all  cases.  Should 
only  a  single  line  of  a  substance  be  found  in  the  spectrum  of 
a  star  or  nebula,  it  would  hardly  be  safe  to  conclude  from  that 
alone  that  the  line  was  really  produced  by  the  known  sub- 
stance. Collateral  evidence  might,  however,  come  in.  If  the 
same  line  were  found  both  in  the  sunlight  and  in  that  of  a 
great  number  of  stars,  we  should  be  justified  in  concluding 
that  the  lines  were  all  produced  by  the  same  substance.  All 
we  can  say  in  doubtful  cases  is,  that  our  conclusions  must  be 
drawn  with  care  and  discrimination,  and  must  accord  with  the 
probabilities  of  each  special  case. 


PABT  III.  —  THE  SOLAR  SYSTEM. 


CHAPTER  I. 

GENERAL    STRUCTURE    OF     THE    SOLAR    SYSTEM. 

Having,  in  the  preceding  parts,  described  the  general  stniet* 
nre  of  tlie  universe,  and  the  methods  used  by  astronomers  in 
measuring  tlie  lieavens  and  investigating  the  celestial  motions, 
we  have  next  to  consider  in  detail  the  separate  bodies  which 
compose  the  universe,  and  to  trace  the  conclusions  respecting 
the  general  order  of  ci-eation  to  which  this  examination  may 
lead  us.  Our  natural  course  will  be  to  begin  with  a  general 
description  of  the  solar  system  to  which  our  earth  belongs, 
considering,  first,  tlie  great  central  body  of  that  system,  then 
the  planets  in  their  order,  and,  lastly,  such  irregular  bodies  as 
comets  and  meteors. 

We  have  shown  in  the  fii'st  part  that  the  solar  system  was 
found  by  Copernicus,  Kepler,  and  Xewton  to  consist  of  tlie 
sun,  as  the  great  central  body,  with  a  number  of  planets  re- 
volving around  it  in  ellipse?,  having  the  sun  in  one  of  their 
foci;  the  whole  being  bound  together  by  the  law  of  universal 
gravitation.  Modern  science  has  added  a  great  number  of 
bodies,  and  shown  the  system  to  be  a  much  more  complex  one 
than  Newton  supposed.  As  we  now  know  them,  the  bodies 
of  the  system  may  be  classiiled  as  follows : 

1.  The  sun,  the  great  central  body ; 

2.  A  group  of  four  inner  planets  —  Mercury,  Venus,  the 
Earth,  and  Mars ; 

3.  A  swai-m  of  small  planets  or  asteroids  revolving  outside 
the  orbit  of  Mars  (about  220  of  them  are  now  known) ; 


232 


TEE  SOLAR  SYSTEM. 


4.  A.  group  of  four  outer  planets — Jupiter,  Saturn,  Uranus, 
and  Nepcune ; 

5.  A  number  of  satellites  of  the  planets,  20  boins;  now 
known,  of  which  all  but  three  belong  to  the  group  of  outer 
planets ; 


Fig.  01.— Relative  size  of  sim  and  planets. 

6.  An  unknown  number  of  comets  and  meteors,  revolving 
in  ver}'  eccentric  orbits. 

The  eight  planets  of  groups  2  and  -i  are  called  the  major 
planets,  to  distinguish  them  from  all  others,  which  are  smalle! 
or  less  important. 


GENERAL  STRUCTURE  OF  THE  SOLAR  SYSTEM. 


233 


The  range  of  size,  distance,  and  mass  among  the  bodies  of 
the  system  is  enormous.  Xeptnne  is  eighty  times  as  far  from 
the  sun  as  Mercury,  and  Jupiter  several  thousand  times  as 
heavy.  It  is,  therefore,  difhcult  to  lay  down  a  map  of  the 
whole  system  on  the  same  scale.  If  the  orbit  of  Mercury  were 
represented  with  a  diameter  of  one-fourth  of  an  inch,  that  of 
Keptune  would  have  a  diameter  of  20  inches. 

With  the  exception  of  Neptune,  the  distances  of  the  eight 
major  planets  proceed  in  a  tolerably  regular  progrcssion,  the 
group  of  small  planets  taking  the  place  of  a  single  planet  in 
the  series.  Tlie  progression  is  known  as  the  law  of  Titius, 
from  its  first  proposer,  and  is  as  follows :  Take  the  series  of 
numbers  0,3,  6,  12,  24,  48,  each  one  after  the  second  being 
formed  by  doul)ling  the  one  which  precedes  it.  Add  4  to 
each  of  these  numbers,  and  we  shall  have  a  series  of  numbers 
giving  very  nearly  the  relative  distances  of  the  planets  from 
the  sun.  The  following  table  shows  the  series  of  numbei-s  thus 
formed,  together  with  the  actual  distances  of  the  planets  ex- 
pressed on  the  same  scale,  the  distance  of  the  earth  being 
called  10 : 


Planet. 

Numbers  of  Titiu3. 

Actual  Distance. 

Error. 

Mercui'v 

0  +  4=      4 

3  +  4=      7 

6  +  4=    10 

12+4=    16 

24  +  4  =    28 

48  +  4  =    52 

96  +  4  =  100 

192  +  4  =  196 

384  +  4  =  388 

3.!) 

7.2 

10.0 

15.2 

20  to  35 

52.0 

95.4 

191.9 

300.6 

0.1 
0.2 
0.0 

0.8 

0.0 
4.G 
4.1 

87.4 

Venus 

Earth 

Mars 

Minor  planets 

Jupiter 

Saturn 

Uranus 

Neptune 

It  will  be  seen  that  before  the  discovery  of  Neptune  the 
agreement  was  so  close  as  to  suggest  the  existence  of  an  actual 
law  of  the  distances.  But  the  discovery  of  this  planet  in  1S46 
completely  disproved  the  supposed  law ;  and  there  is  now  no 
reason  to  believe  that  the  proportions  of  the  solar  system  are 
the  result  of  any  exact  and  simple  law  whatever.  It  is  true 
that  many  ingenious  people  employ  themselves  from  time  to 
time  in  working  out  numerical  relations  between  the  distances 
of  the  planets,  their  masses,  their  times  of  rotation,  and  so  on. 


234  THE  SOLAR   SYSTEM. 

and  will  probably  continue  to  do  so ;  because  the  number  of 
such  relations  which  can  be  made  to  come  somewhere  near  to 
exact  numbei-s  is  very  great.  This,  however,  does  not  indicate 
any  law  of  nature.  If  we  take  forty  or  fifty  numbers  of  an}' 
kind — say  the  years  in  which  a  few  persons  were  born ;  their 
ages  in  years,  months,  and  days  at  some  particular  event  in 
their  lives;  the  numbei'S  of  the  houses  in  which  they  live;  and 
so  on — we  should  find  as  many  curious  relations  among  the 
numbers  as  have  ever  been  found  among  those  of  the  planet- 
ary system.  Indeed,  such  relations  among  the  years  of  the  lives 
of  great  actors  in  the  world's  history  will  be  remembered  by 
many  readers  as  occurring  now  and  then  in  the  public  journals. 
Range  of  Planetary  Masses. — The  great  diversity  of  the  size 
and  mass  of  the  planets  is  shown  by  the  curious  fact,  that,  con- 
sidering the  sun  and  the  eight  planets,  the  mass  of  each  of  the 
nine  bodies  exceeds  the  combined  mass  of  all  those  which  are 
smaller  than  itself.  This  is  shown  in  the  following  simple  cal- 
culation. Suppose  the  sun  to  be  divided  into  a  thousand  mill- 
ions of  equal  parts,  one  of  which  parts  we  take  as  the  unit  of 
weight:  then,  according  to  the  best  determinations  yet  made, 
the  mass  of  each  planet  will  be  that  used  in  the  following  cal- 
culation, in  which  each  mass  is  added  to  the  masses  of  all  the 
planets  which  are  smaller  than  itself,  the  planets  being  taken 
in  the  order  of  their  masses,  beginning  with  the  smallest : 

Mass  of  Mercuiy 200 

Mass  of  Mars 339 

Combined  mass  of  Mercury  and  Mars .^39 

Mass  of  Venus 2,353 

Combined  mass  of  Mercuiy,  Venus,  and  Mars 2,892 

Mass  of  tbe  Earth ." 3,000 

Combined  mass  of  the  four  inner  planets 5,;>52 

Mass  of  Uranus 44,250 

Combined  mass  of  five  planets 50,202 

Mass  of  Neptune 51. GOO 

Combined  m.ass  of  six  planets 101.802 

Mass  of  Saturn 285.580 

Combined  mass  of  seven  planets 387.382 

Mass  of  Jupiter 954,305 

Combined  mass  of  all  the  planets 1,341,687 

Mass  of  the  sun 1,000,000,000 


ASPECTS  OF  THE  PLANETS.  235 

It  will  be  seen  that  the  combined  mass  of  all  the  planets  is 
less  than  rhj  that  of  the  sun ;  that  Jupiter  is  between  two  and 
three  times  as  heavy  as  the  other  seven  planets  togetlier;  Sat- 
urn more  than  twice  as  heavy  as  the  other  six ;  and  so  on. 

Aspects  of  the  Planets. — The  apparent  motions  of  the  plan- 
ets are  described  in  the  first  chapter  of  this  work ;  and  in  tJie 
second  chapter  it  is  shown  how  these  apparent  motions  result 
from  the  real  motions  as  laid  down  by  Copernicus.  The  best 
time  to  see  one  of  the  outer  planets  is  when  in  opposition  to 
the  sun.  It  then  rises  at  sunset,  and  passes  the  meridian  at 
midniglit.  Between  sunset  and  midnight  it  will  be  seen  some- 
where between  east  and  south.  Dnring  the  three  months  fol- 
lowing the  day  of  opposition,  the  planet  will  rise  from  three 
to  six  minutes  earlier  every  day.  A  month  after  opposition,  it 
will  be  two  to  three  hours  high  soon  after  sunset,  and  will  pass 
the  meridian  between  nine  and  ten  o'clock  at  night;  while 
three  months  after  opposition,  it  will  be  on  the  meridian  about 
six  in  the  evening.  Hence,  knowing  when  a  planet  is  in  op- 
position, a  spectator  will  know  pretty  nearly  where  to  look  for 
it.  His  search  will  be  facilitated  by  the  use  of  a  star  map 
showing  the  position  of  the  ecliptic  among  the  stars,  because 
the  planets  are  always  very  near  the  ecliptic.  Indeed,  if  any 
bright  star  is  not  down  on  the  map,  he  may  feel  sure  that  it  is 
a  planet. 

In  describing  the  individual  planets,  we  give  the  times  when 
the}'  are  in  opposition,  so  that  the  reader  may  always  be  able 
to  recognize  them  at  favorable  seasons,  if  he  wishes  to  do  so. 

The  arrangement  of  the  planets,  with  their  satellites,  is  as 
follows : 


Imneb  Gkoop.. 


flMercmy. 
Venus. 
Earth,  with  its  moon. 
Mars,  with  2  moons. 

The  minor  planets,  or  asteroids. 

r  Jupiter,  with  4  moons. 
Outer  Gkoup  of  J  Saturn,  witli  lings  and  8  moons. 
Great  Planets.   I  u.-anus,  with  4  moons. 

^  Neptune,  with  1  moon. 


236 


THE  SOLAR  SYSTEM. 


This  ai-rangeinent  is  partly  exhibited  in  the  following  plan 
of  the  solar  system,  showing  the  relations  of  the  planetary  or- 
bits from  the  earth  outward.  The  scale  is  too  small  to  show 
the  orbits  of  Mercury  and  Venus. 

,    of  yeptune 

oiSi- — 


of  ITranns 


Fig.  62 Orbits  of  the  plauets  from  the  earth  outward,  showing  their  relative  distances 

from  the  suu  iu  the  centre.    The  positions  of  the  planets  are  near  those  which  they  oo 
oupy  in  1S77. 


THE  PHOTOSPHERE.  237 


CHAPTER  IT. 

THE    SUN. 

The  sun  presents  to  our  view  the  aspect  of  a  brilliant  globe 
32',  or  a  little  more  than  half  a  degree,  in  diameter.  To  give 
precision  to  our  language,  the  shining  surface  of  this  globe, 
which  we  see  with  the  eye  or  with  the  telescope,  and  which 
forms  the  visible  sun,  is  called  the  photosphere.  Its  light  ex- 
ceeds in  intensity  any  that  can  be  produced  by  artificial 
means,  the  electric  light  between  charcoal  points  being  the 
only  one  which  does  not  look  absolutely  black  against  the  un- 
clouded sun.  Onr  knowledge  of  the  natui-e  of  this  Innnnary 
commences  with  the  invention  of  the  telescope,  since  without 
this  instrument  it  was  impossible  to  form  any  conception  of 
its  constitution.  The  ancients  had  a  vague  idea  that  it  was  a 
globe  of  fire,  and  in  this  they  were  more  nearly  right  than 
some  of  the  moderns  ;  but  there  was  so  entire  an  absence  of 
all  real  foundation  for  their  opinions  that  the  latter  are  of  lit- 
tle interest  to  any  one  but  the  historian  of  philosophy.  We 
shall,  therefore,  commence  our  description  of  the  sun  with  a 
consideration  of  the  telescopic  researches  of  recent  times. 

§  1.   The  Photosphere  and  Solar  Radiation. 

To  the  naked  eye  the  photosphere,  or  shining  surface  of  the 
sun,  presents  an  aspect  of  such  entire  uniformity  that  any  at- 
tempt to  gain  an  insight  into  its  structure  seems  hopeless. 
But  when  we  apply  a  telescope,  we  generally  find  it  diversified 
with  one  or  more  groups  of  dark-looking  spots ;  and  if  the  vis- 
ion is  good,  and  we  look  carefully,  we  shall  soon  see  that  the 
whole  bright  surface  presents  a  mottled  appearance,  looking 
like  a  fluid  in  which  ill-defined  rice-grains  are  suspended.  Per- 
haps the  most  familiar  idea  of  this  appeai'ancc  will  be  pre- 


238  THE  SOLAR   SYSTEM. 

sented  by  saying  that  the  sim  looks  like  a  plate  of  rice  soup, 
the  grains  of  rice,  however,  being  really  hundreds  of  miles  in 
length.  Some  years  ago  Mr.  Xasmyth,  of  England,  examining 
the  sun  with  high  telescopic  poAvei-s,  announced  that  this  mot- 
tled appearance  seemed  to  him  to  be  produced  by  the  inter- 
lacing of  long,  narrow  objects  shaped  like  willow  leaves,  which, 
running  and  crossing  in  all  directions,  form  a  net-work,  cover- 
ing the  entire  photosphere.  TJiis  view,  though  it  has  become 
celebi'ated  through  the  very  great  care  which  Mr.  Nasuiyth 
devoted  to  his  observations,  has  not  been  confirmed  by  subse- 
quent observers. 

Among  the  most  careful  and  laborious  telescopic  studies  of 
the  sun  recently  made  are  those  of  Professor  Langley.*  He 
has  a  fine  telesco^je  at  his  command,  in  a  situation  where  the 
air  seems  to  be  less  disturbed  by  the  sun's  rays  than  is  usual 
in  other  localities.  According  to  his  observations,  when  the 
sun  is  carefully  examined,  the  mottling  which  Me  have  de- 
scribed is  seen  to  be  caused  by  an  appearance  like  fleecy 
clouds  whose  outlines  are  nearly  indistinguishable.  We  may 
also  discern  numerous  faint  dots  on  the  white  backgi-ound. 
Under  high  powers,  used  in  favorable  moments,  the  surface 
of  any  one  of  the  fleecy  patches  is  resolved  into  a  congeries 
of  small,  intensely  bright  bodies,  irregularly  distributed,  which 
seem  to  be  suspended  in  a  comparatively  dark  medium,  and 
whose  definitcness  of  size  and  outline,  though  not  absolute,  is 
yet  striking,  by  contrast  with  the  vagueness  of  the  cloud-like 
forms  seen  before,  and  which  we  now  perceive  to  be  due  to 
their  aggregation.  The  "dots"  seen  before  are  considerable 
openings,  caused  by  the  absence  of  the  white  nodules  at  cer- 
tain points,  and  the  consequent  exposure  of  the  gray  medium 
which  forms  the  general  background.  These  openings  have 
been  called  pores.  Tiieir  variety  of  size  makes  any  measure- 
ments nearly  valueless,  though  we  may  estimate  in  a  very 
rougli  way  the  diameter  of  the  more  conspicuous  at  from  2" 
to  4".       " 

*  Professor  S.  P.  Langley,  Director  of  the  Observatory  at  Allegheny,  Pennsyl- 
vania. 


THE  PHOTOSPHEEE.  239 

In  moments  when  the  definition  is  very  fine,  the  hright  nod- 
ales  or  rice-grains  are  found  to  be  made  up  of  clusters  of  mi- 
nute points  of  light  or  "gramiles,"  about  one-third  of  a  second 
in  diameter.  These  have  also  been  seen  around  the  edges  of 
the  pores  by  Secchi,  who  estimated  their  magnitude  as  even 
less  than  that  assigned  by  Langley.  The  fact  that  these  points 
are  aggregated  into  little  clusters,  which  ordinarily  present  the 
appearance  of  rice-grains,  gives  the  latter  a  certain  irregulari- 
ty of  outline  which  has  been  remarked  by  Mr.  Iluggius.  Tluis, 
there  appear  to  be  three  orders  of  aggregation  in  the  brighter 
regions  of  the  photosphere  :  cloud-like  forms  which  can  be 
easily  seen  at  any  time;  rice-grains  or  nodules, into  which  these 
forms  are  resohed,  and  which  can  always  be  seen  with  a  fair 
telescope  under  good  definition;  and  granules  which  make  up 
the  rice-grains.  There  is,  however,  no  sharp  distinction  to  be 
drawn  between  the  nodules  and  the  rice-crains  :  it  might  be 
almost  as  near  the  truth  to  say  that  the  rice-grains  are  of  va- 
rious sizes,  ranging  from  one-third  of  a  second  in  dianieter  to 
one  second  or  more,  and  that  the  smaller  ones  arc  often  col- 
lected into  minute  clusters,  which  can  hardly  be  distinguished 
from  grains  of  larger  size. 

Yet  more  recent  are  the  studies  of  the  sun's  surface  made 
by  Jaussen,*  of  France,  with  the  aid  of  photography.  This 
method  has  a  great  advantage  in  the  strength  and  perma- 
nency of  the  photographic  record,  and  the  consequent  power 
of  studying  it  at  leisure.  A  disadvantage  arises  from  the 
great  foe  of  astronomical  observation  which  we  have  already 
described  —  atmospheric  undulations,  which  render  the  sun's 
image  tremulous  and  confused  except  at  occasional  moments. 
This  difhculty  may,  however,  be  obviated  by  taking  a  great 
mnnber  of  photographs,  and  selecting  those  which  show  the 
best  images. 

In  applying  this  method,  Janssen  has  taken  his  photographs 
on  a  larger  scale  than  has  been  attempted  by  his  predecessors, 
his  largest  pictures  of  the  sun  being  from  twel\e  to  fifteen 


*  Prof.  J.  C.  Janssen,  director  of  the  plivsical  observatory  at  Jleudon,  France. 

17 


240  THE  SOLAR  SYSTEM. 

inches  in  dianietei".  The  granulation  is  thus  brought  out  with 
remarkable  distinctneos,  as  may  be  seen  from  the  following 
^!gure,  which  is  enlarged  so  that  the  whole  sun,  on  the  same 
scale,  M'onld  be  three  feet  in  diameter. 


Fig.  C3. —  Aspect  of  the  Sim's  Surface  as  Photographed  by  Jaiisseu  at  the  Obseivatory 

of  Mendon. 

M.  Jansscn  finds  that  the  granular  elements  are  of  very  dif- 
ferent sizes  and  brilliancy,  the  diameters  ranging  from  a  few 
tentlis  of  a  second  to  three  or  four  seconds.  The  form  is  gen- 
erally slightly  elliptic,  but  is  subject  to  considerable  variations. 
The  differences  of  brilliancy  among  the  granules  seem  to  arise 
from  their  being  situated  at  different  depths  in  the  photo- 
spliere.  But  the  most  remarkable  i-esult  of  Janssen's  photo- 
graphs is  what  he  calls  the  photospheric  net -work,  '"'■  reseaxi 
])liotospheriqueP  This  is  not  a  net-work  of  lines,  as  we  miglit 
understand  it,  but  a  subdivision  of  the  photosphere  into  region?. 
in  which  the  granules  look  hard  and  well  defined,  and  regions 
in  whicli  they  look  softened  and  indistinct.  This  ap))earance 
is  shown,  though  somewhat  imperfectly,  in  the  above  figure, 


THE  PHOTOSPHERE.  241 

which  is  taken  from  one  of  Janssen's  photographs.  The  boun- 
daries of  the  regions  of  well  and  ill  defined  granulations  are 
necessarily  somewhat  indefinite,  and  sometimes  appear  straight 
and  sometimes  curved.  The  dimensions  of  the  regions  of  ill- 
defined  granulation  are  very  variable.  Sometimes  they  attain 
a  diameter  of  one  minute  or  more.  Within  them,  the  granules 
sometimes  disappear  entirel}',  their  place  being  occupied  by 
streams  of  matter.  This  disappearance  seems  to  be  due  to 
violent  movements  of  the  photospheric  matter  destroying  the 
granular  elements. 

"When  we  call  these  shining  objects  "granules,"  it  must  be 
remembered  tliat  we  speak  of  the  appearance,  not  of  the  reali- 
ty. To  subtend  an  angle  of  one  second,  at  the  distance  of  the 
sun,  a  line  must  be  450  miles  long ;  consequently,  from  what 
is  said  of  the  size  of  the  granules,  they  must  be  from  100  to 
500  miles  in  length  and  breadth. 

If  we  carefully  examine  the  sun  with  a  very  dark  smoked 
glass,  we  shall  find  that  the  disk  is  brightest  at  the  centre, 
shading  off  on  all  sides  towards  the  limb.  Careful  compari- 
sons of  the  intensity  of  radiation  of  different  parts  of  the  disk 
show  that  this  diminution  near  the  limb  is  common  to  all  the 
rays,  whether  those  of  heat,  of  light,  or  of  chemical  action. 
The  most  recent  measures  of  the  heat  rays  were  made  by 
Langley  by  means  of  a  thermo-electric  pile,  those  of  the  light 
i-ays  by  Pickering,^  and  those  of  the  chemical  rays  by  Yogel.f 
Tlie  intensities  of  these  several  radiations  at  different  distances 
from  the  centre  of  tlie  disk  as  thus  determined  are  shown  in 
the  table  on  the  following  page.  The  intensity  at  the  centre 
is  always  supposed  100.  The  first  column  gives  the  distance 
from  the  centre  in  fractions  of  the  sun's  radius,  which  is  sup- 
posed unity.  Thus,  the  first  line  of  the  table  corresponds  to 
tlie  centre ;  the  last  to  the  edge.  Professor  Langley's  meas- 
ures do  not,  however,  extend  to  the  extreme  edge. 

*  Professor  E.  C.  Pickering,  Director  of  tlie  Harvard  Observatory,  Cambridge, 
Massachusetts. 

t  Dr.  Hermann  C.  Vogel,  formerly  astronomer  at  Botiiliamp,  now  of  the  Solar 
Observatory  in  Potsdam,  Prussia. 


242 


THE  SOLAR  SYSTEM. 


Distance  from 

Heat  Rays 

Light 

Chemical  Ravs 

Centre  of  the  Snn. 

(Langley). 

(Pickering). 

(Vogel).  ■ 

.00 

100 

100 

100 

.125 

99 

100 

.25 

99 

97 

98 

.375 

94 

95 

.50 

"95 

91 

90 

.625 

86 

81 

.75 

86 

79 

66 

.85 

69 

48 

.95 

55 

25 

.96 

"62 

... . 

23 

.98 

50 

18 

1.00 

"37 

13 

It  will  be  seen  that  near  the  edge  of  the  disk  the  chemical 
rays  fall  off  most  rapidly,  the  light  rays  next,  and  the  heat 
i-ays  least  of  all.  Roughly  speaking,  each  square  minute  near 
the  limb  of  the  sun  gives  about  half  as  much  heat  as  at  the 
centre,  about  one-third  as  much  light,  and  less  than  one-seventh 
as  many  photographic  rays.  Of  the  cause  of  this  degradation 
of  light  and  heat  towards  the  limb  of  the  sun  no  doubt  has 
been  entertained  since  it  was  first  investigated.  It  is  found  in 
the  absorption  of  the  rays  by  a  solar  atmosphere.  The  sun 
being  a  globe  surrounded  by  an  atmosphere,  the  rays  which 
emanate  from  the  photosphere  in  a  horizontal  direction  have 
a  greater  thickness  of  atmosphere  to  pass  through  than  those 
which  strike  out  vertically ;  while  the  former  are  those  we 
see  near  the  edge  of  the  disk,  and  the  latter  near  the  centre. 
The  different  absorptions  of  different  classes  of  rays  corre- 
spond exactly  to  this  supposition,  it  being  known  that  the 
more  refrangible  or  chemical  rays  are  most  absorbed  by  va- 
pors, and  the  heat  rays  the  least. 

Fi'om  this  it  follows  that  we  get  but  a  fraction — perhaps  a 
small  fraction — of  the  light  and  heat  actually  emitted  by  the 
sun ;  and  that  if  the  latter  had  no  atmosphere,  it  would  bo 
much  hotter,  much  brighter,  and  bluer  in  color,  than  it  actually 
is.  The  total  amount  of  absorption  has  been  very  differently 
estimated  by  different  authorities,  Laplace  supposing  it  might 
be  as  much  as  eleven  -  twelfths  of  the  whole  amount.  The 
smaller  estimates  are,  however,  more  likely  to  be   near  the 


THE  PHOTOSPHERE.  243 

truth,  there  being  no  good  reason  for  holding  that  more  than 
half  the  rajs  are  absorbed.  That  is,  if  the  sun  liad  no  atmos- 
phere, it  might  be  twice  as  bright  and  as  liot  as  it  actually  is, 
but  would  not  be  likely  to  be  three  or  four  times  so.  Profess- 
or Langley  suggests  that  the  glacial  epocli  may  have  been  due 
to  a  greater  absorption  of  the  sun's  heat  by  its  atmosphere  in 
some  past  geological  age. 

A  \Q.Yy  important  physical  and  astronomical  problem  is  that 
of  measuring  the  total  amount  of  heat  radiated  by  the  sun  to 
the  earth  during  any  period  of  time  —  say  a  day  or  a  year. 
The  question  admits  of  a  perfectly  definite  answer,  but  there 
are  two  difficulties  in  the  way  of  obtaining  it;  one,  to  distin- 
guish between  the  heat  coming  from  the  sun  itself,  and  that 
coming  from  the  atmosphere  and  surrounding  objects;  the 
other,  to  allow  for  the  absorption  of  the  solar  heat  by  our  at- 
mosphere, which  must  be  done  in  order  to  determine  the  to- 
tal quantity  emanating  from  the  sun.  The  standard  determi- 
nations have  long  been  considered  those  of  Pouillet  and  of  Sir 
John  Ilcrschel.  The  results  obtained  by  the  former  may  bo 
expressed  thus:  if  the  air  were  out  of  the  way,  and  a  sheet  of 
ice  were  so  held  that  the  sun's  rays  should  fall  upon  it  per- 
pendicularly, and  be  all  absorbed,  the  ice  would  melt  away  at 
the  rate  of  14^  inches  in  24  hours.  But  Professor  Langley 
has  recently  shown  that  this  result  is  much  too  small,  owing 
to  the  absorbing  power  of  the  earth's  atmosphere  being  under- 
estimated. The  increase  has  not  been  accuratel}'  determined, 
but  is  probably  50  per  cent.,  and  may  be  yet  greater. 

Attempts  have  been  made  to  determine  the  temperature  of 
the  sun  from  the  amount  of  heat  which  it  radiates,  but  the 
estimates  have  varied  very  widely,  owing  to  the  uncertainty 
respecting  the  law  of  radiation  at  high  temperatures.  By  sup- 
posing the  radiation  proportional  to  the  temperature,  Secchi* 
finds  the  latter  to  be  several  million  degrees,  while,  by  taking 
another  law  indicated  by  the  experiments  of  Dulong  and 
Petit,  others  find  a  temperature  not  many  times  exceeding 

*  Father  Angelo  Seccbi,  late  Director  of  the  Observatory  at  liome. 


244  THE  SOLAR  SYSTEM. 

that  ot  a  reverberatory  furnace.  For  the  temperature  of  tht 
photosphere,  it  seems  likely  that  the  lower  estimates  ai'e  more 
nearly  right,  being  founded  on  an  experimental  law ;  but  the 
temperature  of  the  interior  must  be  immensely  higher. 

At  the  present  time  an  investigation  of  the  solar  radiation, 
by  Professor  Langley,  is  in  progress,  and  promises  important 
results  as  to  the  actual  amount  of  energy  lost  by  the  sun  every 
year,  and  the  character  of  the  absorption  which  takes  place 
in  the  atmospheres  of  the  sun  and  the  earth.  The  great 
difficulty  met  Avith,  by  previous  investigators,  is  that  obser- 
vations on  the  solar  light  and  heat  have  been  made  near  the 
earth's  surface,  after  the  passage  of  the  rays  through  a  dense 
and  frequently  vaporous  atmosphere.  In  concluding,  from 
measures  at  the  earth's  surface,  the  amount  of  radiation  which 
■would  be  observed  if  there  were  no  atmosphere,  it  is  necessary 
to  make  allowance  for  atmospheric  absorption.  In  calculating 
this  absorption  it  has  been  assumed  p^roportional  to  the  amount 
of  atmosphere  through  which  the  rays  had  passed.  Professor 
Langley  shows  that  altliough  this  assumed  law  may  be  true 
for  i-ays  of  any  one  degree  of  refrangibility,  it  will  not  be  true 
for  the  sun's  heat  as  a  whole ;  because  a  large  absorption  of 
certain  rays,  especially  the  more  refrangible  ones,  takes  place 
in  the  higher  regions  of  the  atmosphere.  In  order  to  attain  a 
good  result  it  was  necessary  to  make  observations  at  the  great- 
est possible  height,  and  in  the  purest  and  dryest  atmosphere, 
and  to  compare  them  with  observations  at  a  lower  station. 

In  1  SSI,  Professor  Langley  organized  an  expedition  to  Mt. 
"Whitney,  in  California,  which  rises  about  15,000  feet  above  the 
level  of  the  sea,  in  a  country  where  the  sky  is  exceptionally 
clear,  and  the  air  unusually  free  from  vapor.  His  measures 
of  temperature  were  made  by  means  of  the  Bolometer,  an  instru- 
ment of  his  own  invention,  especially  adapted  to  this  purpose. 
Its  most  essential  part  is  a  strip  of  metallic  leaf  ^  of  an  inch 
long,  YJT  of  an  inch  wide,  and  ^g^^^  of  an  inch  thick.  This 
minute  object  formed  p>art  of  an  electric  circuit,  and  clianges 
in  its  temperature  were  determined  by  the  consequent  change 
iu  its  electric  conductivity;  so  sensitive  is  it  that  a  change  of 


246  THE  SOLAE  SYSTEM. 

temperature  of  ^  ^  ^^„  ^  (,  of  a  degree  can  be  detected  by  the 
galvanometer. 

This  strip,  being  placed  parallel  to  the  Fraunhofer  lines,  is 
moved  ever  different  parts  of  the  spectrum,  not  only  from  the 
extreme  violet  to  the  extreme  red,  but  yet  farther  among  the 
invisible  heat  rays,  so  long  as  any  radiant  heat  can  be  detected. 
It  is,  therefore,  a  sort  of  an  eye,  which  is  sensitive  to  radiant 
heat  of  all  degrees  of  refrangibility.  "When,  in  moving  slowly 
over  the  spectrum,  it  reaches  a  dark  line,  the  strip  becomes 
slightly  colder,  and  hence  a  better  conductor  of  electricity. 
The  flow  of  electricity  is  therefore  increased.  On  leaving  the 
line  it  grows  warmer,  and  the  flow  of  electricity  is  diminished. 
Thus  the  positions  of  the  lines  are  registered,  whether  they  are 
or  are  not  visible  to  the  human  eye. 

Professor  Langley  has  supplied  figures  showing  the  distribu- 
tion of  the  heat  spectrum  as  thus  determined  on  Mt.  "Whitney. 
The  difference  between  the  two  figures  arises  from  the  dif- 
ferent ways  in  which  the  spectrum  is  formed  by  the  grating 
and  by  the  prism.  The  latter  crowds  together  the  light  or  heat 
waves  of  small  refrangibility  and  long  wave-lengths,  while  it 
proportionally  scatters  rays  of  large  refrangibility  and  short 
wave-lengths.  This  effect  is  shown  in  the  small  figure  B, 
where  the  rays  are  more  and  more  crowded  as  we  pass  from 
the  violet  towards  the  red.  The  corresponding  prismatic  spec- 
trum shows  a  maximum  of  heat  to  the  left  of  the  line  A,  and 
therefore  beyond  the  visible  part  of  the  spectrum. 

It  is  very  different  with  a  diffraction  spectrum  obtained  from 
a  ruled  grating.  Here,  as  will  be  seen  at  A,  the  rays  are  all 
scattered  equally,  so  that  the  spectrum  is  shown  in  its  true 
proportions.  In  the  larger  figure  of  the  diffraction  spectrum 
the  distribution  of  heat  is  shown  on  the  same  scale,  and  the 
maximum  of  heat  is  found  to  be  near  the  orange.  The  bending 
curve  shows  the  intensity  of  the  radiant  heat  at  each  point 
of  the  spectrum,  as  it  would  be  in  the  absence  of  selective 
absorption  by  the  sun's  atmosphere.  "We  have  already  men- 
tioned Professor  Langley's  conclusion  that  the  real  sun, 
below   its   absorbing  layer,  is   much  bluer  than   it   appears 


248  THE  SOLAR  SYSTEM. 

to  US.  But,  from  his  experiments  on  absorption  by  the  earth*8 
atmospliere,  he  also  conchides  that,  cor.lJ  we  rise  above  our  at- 
mosphere, the  sun  would  be  far  richer  in  the  extreme  violet  rays 
than  we  ever  see  it  on  the  earth's  surface,  and  would  appear 
of  a  blue  like  that  of  the  spectrum  near  the  Fraunhofer  line  F. 

§  2.  The  Sola?-  Sjjots  and  Rotation. 

Even  the  poor  telescopes  made  by  the  contemporaries  of 
Galileo  could  liardly  be  directed  to  the  sun  many  tin)es  with- 
out one  or  more  spots  being  seen  on  his  surface.  Whatever 
credit  may  be  due  for  a  discovery  which  required  neither  in- 
dustry nor  sldll  should,  by  the  rule  of  modern  science  already 
referred  to,  be  awarded  to  Fabritius  for  the  discovery  of  the 
solar  spots.  This  observei',  otherwise  unknown  in  astronomy, 
made  known  the  existence  of  the  solar  spots  early  in  IGll — ■ 
a  year  after  Galileo  began  to  scan  the  heavens  with  his  tel- 
escope. His  discovery  was  followed  up  b}'  Galileo  and  Schei- 
ner,  by  whom  the  lirst  knowledge  of  the  nature  of  the  spots 
was  acquired. 

The  first  idea  of  Scheiner  was  that  the  spots  were  small 
planets  in  the  neighborhood  of  the  sun  ;  but  this  was  speedily 
disproved  by  Galileo,  who  showed  that  they  must  be  on  the 
surface  of  the  sun  itself.  The  idea  of  the  smi  being  affected 
w'ith  any  imperfection  so  gross  as  a  dark  spot  was  repugnant 
to  the  ecclesiastical  philosophy  of  the  times,  and  it  is  not  un- 
likel}'  that  Scheiner's  explanation  was  suggested  by  the  desire 
to  save  the  perfection  of  our  central  luminary. 

A  very  little  observation  showed  that  the  spots  had  a  regu- 
lar motion  across  the  disk  of  the  sun  from  east  to  west,  occu- 
pying about  12  days  in  the  transit,  A  spot  generally  appeared 
lirst  on  or  near  the  east  limb,  and,  after  12  or  14  days,  disap- 
peared at  the  west  limb.  At  the  end  of  another  14  days  or 
more  it  reappeared  at  the  east  limb,  unless  in  the  mean  time 
it  had  vanished  from  sight  entirely.  The  spots  were  found 
not  to  be  permanent  objects,  but  to  come  into  existence  from 
time  to  time,  and,  after  lasting  a  few  days,  weeks,  or  months, 
to  disappear.      But  so  long  as  they  lasted,  they  always  ex- 


THE  SOLAR  SPOTS  AND  EOTATIOX. 


240 


hibited  the  motion  just  described,  and  it  was  thence  inferred 
that  the  sun  rotated  on  his  axis  in  about  25  days. 

The  astronomers  of  the  seventeenth  and  eighteenth  centuries 
used  a  method  of  observing  the  sun  which  will  often  be  found 
convenient  for  seeing  the  spots  when  one  lias  not  a  telescope 
supplied  with  dark  glasses  at  his  disposal.  Take  an  ordinary 
good  spy-glass,  oi-,  indeed,  a  telescope  of  any  size,  and  point 


Fig.  05.  —  Method  of  holdiDg  telescope,  to  show  sun  on  screen. 

it  at  the  sun.  To  sa\e  the  eyes,  the  right  direction  may  be 
'found  by  holding  a  piece  of  paper  closely  in  front  of  the  eye- 
piece :  when  the  sun  shines  through  the  telescope  on  this  pa- 
per, the  pointing  is  nearly  right.  The  telescope  should  be  at- 
tached to  some  movable  support,  so  that  its  pointing  can  be 
changed  to  the  different  directions  of  the  sun,  and  should  pass 
tln'ough  a  perforation  in  some  sort  of  a  screen,  so  that  the 
sun  cannot  shine  in  front  of  the  telescope  except  by  passing 


250 


THE  SOLAR  SYSTEM. 


through  it.  An  opening  in  a  window-shutter  will  answer  a 
good  purpose,  onl}'  tlie  ra^'s  must  not  have  to  pass  through  the 
glass  of  the  window  in  order  to  reach  the  telescope.  Draw 
out  the  eye-piece  of  the  instrument  about  the  eighth  of  an 
inch  beyond  the  proper  point  for  seeing  a  distant  object. 
Then,  holding  a  piece  of  white  paper  before  the  eye-piece  at 
a  distance  of  from  G  to  12  inches,  an  image  of  the  sun  will  be 
tl'irown  upon  it.  The  distance  of  the  paper  must  be  adjusted 
to  the  distance  the  eye-piece  is  drawn  out.  The  farther  wo 
draw  out  the  eye  -  piece,  the  nearer  the  best  image  will  be 
formed.  Having  adjusted  everything  so  that  the  edge  of  the 
sun's  image  shall  be  sharply  defined,  one  or  more  spots  can 
generally  be  seen.  This  method,  or  something  similar  to  it,  is 
often  used  in  observing  eclipses  and  transits  of  Mercury,  and 
is  very  convenient  when  it  is  desired  to  show  an  enlarged  im- 
age of  the  sun  to  a  number  of  spectators. 

When  powerful  telescopes  were  applied  to  the  sun,  it  was 
found  that  the  spots  v.-ere  not  merely  the  dark  patches  which 
they  first  appeared  to  be,  but  that  they  comprised  two  well- 


FiG.  CO. — iSoliir  spot,  after  ftecclii. 


marked  portions.  The  central  part,  called  the  umbra  or  nvr 
cleus,  is  the  darkest,  and  is  surrounded  by  a  border,  interme- 
diate in  tint  between  the  darkness  of  the  spot  and  the  brill- 


THE  SOLAR  SPOTS  AND  ROTATION.  251 

iancy  of  the  solar  surface.  This  border  is  termed  the  2>eniim- 
hra.  Ordinarily  it  appears  of  a  uniform  gray  tint.  But  when 
carefully  examined  with  a  good  telescope  in  a  very  steady  at- 
mosphere, it  is  found  to  be  striated,  looking,  in  fact,  much  like 
the  bottom  of  a  thatched  roof,  tlie  separate  straws  being  di- 
rected towards  the  interior  of  the  spot.  This  appearance  is 
shown  in  the  figure. 

The  spots  are  extremely  irregular  in  form  and  unequal  in 
size.  They  are  very  generally  seen  in  groups  —  sometimes 
two  or  more  combined  into  a  single  one ;  and  it  frequently 
happens  that  a  large  one  breaks  up  into  several  smaller  ones. 
Tlieir  duration  is  also  extremely  variable,  ranging  from  a  few 
days  to  periods  of  several  months. 

Until  about  a  century  ago,  it  was  a  question  whether  the 
spots  were  not  dark  patches,  like  scoria,  floating  on  the  molten 
surface  of  the  photosphere.  Wilson,  a  Scotch  observer,  how- 
ever, found  that  they  appeared  like  cavities  in  the  photosphere, 
the  dark  part  being  really  lower  than  the  bright  surface  around 
it.  As  a  spot  approached  the  edge  of  the  disk,  he  found  that 
the  penumbra  grew  disproportionately  narrow  on  tlie  side 
nearest  to  the  sun's  centre,  showing  tliat  this  side  of  it  was 
seen  at  a  smaller  angle  than  the  other.  This  effect  of  per- 
spective is  shown  in  Fig.  G7,  where,  near  the  sun's  limb,  the 
side  of  the  penumbra  nearest  us  is  hidden  by  the  photosphere. 
That  the  spots  are  cavities  is  also  shown  by  the  fact  that 
when  a  large  spot  is  exactly  on  the  edge  of  tlie  disk  a  notch 
is  sometimes  seen  there.  The  shaded  penumbra  seems  to 
form  the  sides  of  the  cavity,  while  the  umbra  is  the  invisible 
bottom. 

These  observations  gave  rise  to  the  celebrated  theory  of 
Wilson,  which  is  generally  connected  with  the  name  of  Iler- 
schel,  who  developed  it  more  fully.  The  interior  of  the  sun 
is,  by  this  theory,  a  cool,  dark  body,  surrounded  by  two  layers 
of  clouds.  The  outer  layer  is  intensely  brilliant,  and  forms 
the  visible  photosphere,  while  the  inner  layer  is  darker,  and 
forms  the  umbra  around  the  spots.  The  latter  are  simply 
openings  through  these   clouds,  which   form   from   time   to 


252 


THE  SOLAR   SYSTEAf. 


Fio.  07. — Chaugcs  in  the  aspect  of  a  solar  spot  as  it  crosses  the  sun's  disk,  showing  it  to  be 
a  cavity  in  the  photosphere. 

time,  and  through  which  we  see  the  dark  body  in  the  interior. 
Anxious  that  this  body  should  serve  some  especial  purpose  in 
the  economy  of  creation,  they  peopled  it  with  intelligent  be- 
ings, who  were  protected  from  the  fierce  radiation  of  the  pho- 
tosphere by  the  layer  of  cool  clouds,  but  were  denied  every 
view  of  the  universe  without,  except  such  glimpses  as  they 
might  obtain  through  the  occasional  openings  in  the  photo- 
sphere, which  we  see  as  spots. 

Leaving  out  the  fancy  of  living  beings,  this  theory  account- 
ed very  well  for  apjiearances.  That  the  photosphere  could  not 
be  absolutely  and  wliolly  solid,  liquid,  or  gaseous  seemed  evi- 
dent from  the  nature  of  the  spots.  If  it  were  solid,  the  latter 
could  not  be  in  such  a  constant  state  of  change  as  we  see 


THE  SOLAR  SPOTS  AND  ROTATION.  253 

them ;  wliile  if  it  were  liquid  or  gaseous,  tliese  cavities  could 
not  continue  for  months,  as  they  "vvere  sometimes  seen  to,  be- 
cause tlie  liquid  or  gaseous  matter  would  rush  in  from  all 
sides,  and  till  them  up.  The  oidy  hypothesis  that  seemed  left 
open  to  Ilerschel  was  that  the  photosphere  consisted  of  clouds 
floating  in  an  atmosphere.  As  the  sides  of  the  cavities  looked 
comparatively  dark,  the  conclusion  seemed  inevitable  that  the 
brilliancy  of  the  photosphere  was  only  on  and  near  the  sur- 
face; and  as  the  bottom  of  the  cavity  looked  entirely  dark, 
the  conclusion  that  the  sun  had  a  dark  interior  seemed  una- 
voidable. 

The  discovery  of  the  conservation  of  force,  and  of  the  mut- 
ual convertibility  of  heat  and  force,  was  fatal  to  this  theory. 
Such  a  snn  as  that  of  Ilerschel  would  have  cooled  off  entirely  in 
a  few  days,  and  then  we  should  receive  neither  light  nor  heat 
from  it.  A  continuous  flood  of  heat  such  as  the  sun  has  been 
radiating  for  thousands  of  years  can  be  kept  up  only  by  a  con- 
stant expenditure  of  force  in  some  of  its  forms ;  but,  on  Iler- 
schel's  theory,  the  supply  necessary  to  meet  this  expenditure 
was  impossible.  Even  if  the  heat  of  the  photosphere  could 
be  kept  up  by  any  agency,  it  would  be  constantly  convej^ed  to 
the  interior  by  conduction  and  radiation  ;  so  that  in  time  the 
whole  sun  would  become  as  hot  as  the  photosphere,  and  its 
inhabitants  would  be  destroyed.  In  the  time  of  Ilerschel  it 
was  not  deemed  necessary  that  the  sun  should  be  a  very  hot 
body,  the  heat  received  from  his  rays  being  supposed  by  many 
to  be  generated  by  their  passage  through  our  atmosphere. 
The  photosphere  was,  therefore,  supposed  to  be  simply  phos- 
phorescent, not  hot.  This  idea  is  still  entertained  by  many 
educated  men  who  have  not  made  themselves  acquainted  with 
the  laws  of  heat  discovered  during  the  present  century.  We 
may,  therefore,  remark  that  it  is  completely  untenable.  One 
of  the  best  established  results  of  these  laws  is  that  the  surface 
of  the  sun  is  intensely  hot,  probably  much  hotter  than  any  re- 
verberatory  furnace.  The  great  question  in  the  present  state 
of  science  is,  how  the  supply  of  heat  is  maintained  against 
such  innnense  loss  by  radiation. 


254  TEE  SOLAR  STSTEiT. 

§  3.  Periodicity  of  the  Spots. 

The  careful  observations  of  the  solar  spots  which  have  been 
made  during  the  last  century  seem  to  indicate  a  period  of 
about  eleven  years  in  the  spot-producing  activity  of  the  sun. 
During  two  or  three  years  the  spots  are  larger  and  more  nu- 
merous than  on  the  average ;  they  then  begin  to  diminish, 
and  reach  a  minimum  live  or  six  years  after  the  maximum. 
Another  six  years  brings  the  return  of  the  maximum.  The 
intervals  are,  however,  somewhat  irregular,  and  further  obser- 
vations are  required  before  the  law  of  this  period  can  be  fixed 
with  certainty.  An  idea  of  the  evidence  in  favor  of  the  pe- 
riod may  be  formed  from  some  results  of  the  observations  of 
Schwabe,  a  German  astronomer,  who  systematically  observed 
the  sun  during  a  large  part  of  a  long  life.  One  of  liis  meas- 
ures of  the  spot-producing  power  was  the  number  of  days  on 
which  he  saw  the  sun  without  spots  in  the  course  of  each 
year.     The  following  are  some  of  his  results : 

From  1828  to  1831,  sun  without  spots  on  only  1  day. 

In  1833,  "  "  "  139  days. 

From  1836  to  1840,  "  "  "  3  days. 

In  18i3,  "  "  "  147  days. 

From  1847  to  1851,  "  "  "  2  days. 

In  18o6,  "  "  "  193  days. 

From  1858  to  1861,  "  "  "  no  day. 

In  1867,  "  "  "  195  days. 

"We  see  that  the  sun  was  remarkably  free  from  spots  in  the 
years  1833,  1843,  1856,  and  1867,  about  half  the  time  no  con- 
siderable spot  being  visible.  This  recurrence  of  the  period 
has  been  traced  back  by  Dr.  Wolf,  of  Zurich,  to  the  time  of 
Galileo,  and  its  average  length  is  about  11  yeai-s  1  month. 
The  years  of  fewest  sun-spots  during  the  present  century  were 
ISld,  1823,  1833.  1S44,  1856,  and  1867.  Continuing  the 
series,  we  may  expect  very  few  spots  in  1878, 1889,  etc.  The 
years  of  greatest  production  of  spots  were  1804,  1816,  1829, 
1837,  1848,  1860,  and  1870,  from  which  we  may  conclude 
that  1882j  1893,  etc.,  will  be  years  of  numerous  sun-spots. 


PEBIODICITY  OF  THE  SPOTS.  255 

The  observations  of  Scliwabe  and  the  researclies  of  AVolf 
seem  to  have  placed  the  existence  of  tliis  period  beyond  a 
doubt ;  l)ut  no  satisfactory  explanation  of  its  cause  has  yet 
been  <>:iven.  When  first  noticed,  its  near  approacli  to  the  pe- 
riod of  revolution  of  Jupiter  naturally  led  to  the  belief  that 
'here  was  a  connection  between  the  two,  and  that  tlie  attrac 
lion  of  the  largest  planet  of  the  system  produced  some  disturb- 
ance in  the  sun,  wliich  was  greater  in  perihelion  than  in  aphe- 
lion. But  this  connection  seems  to  be  disproved  by  tlie  fact 
that  the  sun-spot  period  is  at  least  six  months,  and  perha])s  a, 
yeai-,  shorter  than  the  revolution  of  Jupiter.  It  is  therefore 
probable  that  the  periodicity  in  question  is  not  due  to  any  ac- 
tion outside  the  sun,  but  is  a  result  of  some  law  of  solar  action 
of  wliich  we  are  as  yet  ignorant. 

There  are  cei-tain  supposed  connections  of  the  sun-spot  pe- 
riod with  teri'estrial  phenomena  wliich  are  of  interest.  Sir 
William  Ilerschel  collected  quite  a  mass  of  statistics  tending  to 
show  that  tliere  was  an  intimate  connection  between  the  num- 
ber of  sun-spots  and  the  price  of  corn,  the  latter  being  low 
when  there  wei-e  few  spots,  and  liigli  when  they  were  more 
numerous.  His  conclusion  was  that  the  fewer  the  spots,  the 
more  favorable  the  solar  rays  to  the  growth  of  tlie  crops. 
This  theory  has  not  been  confirmed  by  subsequent  obsei-va- 
tion.  There  is,  however,  some  reason  to  believe,  from  the 
researches  of  Professors  Levering  and  Loom  is,  that  tlie  fre- 
quency of  auroras  and  of  magnetic  disturbances  is  subject  to 
a  period  corresponding  to  that  of  sun-spots,  these  occurrences 
being  most  frequent  when  the  spots  are  most  numerous.  Pro- 
fessor Loomis  considers  the  coincidence  to  be  pretty  well 
proved,  while  Professor  Levering  is  more  cautious,  and  waits 
for  further  research  before  coming  to  a  positive  conclusion. 
The  occurrence  of  great  auroras  in  1859  and  1S70-'71  was 
strikingly  accordant  with  the  theory. 

§  4.  Law  of  Rotation  of  tlie  San. 

Between  the  years  1843  and  1861,  a  very  careful  series  of 
observations  of  the  positions  and  motions  of  the  solar  spots 

IS 


256  THE  SOLAR  SYSTEM. 

was  made  by  Mr.  Carriiigton,  of  England,  with  a  %-iew  of  de 
diicinic  the  exact  time  in  which  the  sun  rotates  on  liis  axis. 
These  observations  led  to  tlie  remarkable  result  that  the  time 
of  i-otation  shown  by  tlie  spots  was  not  the  same  on  all  i>arts 
of  the  sun,  but  that  the  equatorial  regions  seemed  to  perform 
a  revolution  in  less  time  th;in  those  nearer  the  poles,  Kear 
the  equator  the  period  was  about  25.3  days,  wliile  it  was  a 
day  longer  in  30°  latitude.  Moreover,  the  period  of  rotatiou 
seems  to  be  different  at  different  times,  and  to  vary  with  ths 
frequency  of  the  spots.  But  the  laws  of  these  variations  are 
not  yet  established.  In  consequence  of  their  existence,  we 
cannot  fix  any  delinite  time  of  rotation  for  the  snn,  as  we  can 
for  the  earth  and  for  some  of  the  planetc-.  It  varies  at  dif- 
ferent times,  and  under  different  circumstances,  from  25  to 
2(ji  days. 

The  cause  of  these  variations  is  a  subject  on  which  there  is 
yet  no  general  agreement  among  those  who  have  most  care- 
fully investigated  the  subject.  Zollner*  and  Wolf  see  in  the 
general  motions  of  the  spots  traces  of  currents  moving  from 
bath  poles  of  the  sun  towards  the  equator.  The  latter  con- 
sideia  that  the  eleven -year  spot-period  is  associated  with  a 
Hood  of  liquid  or  gaseous  matter  thrown  np  at  the  poles  of 
the  sun  about  once  in  eleven  years,  and  gradually  iinding  its 
vay  to  the  equator.  Ziilhier  adopts  the  same  theory,  and  has 
bubmittcd  it  to  a  mathematical  analysis, the  basis  of  which  is 
that  the  sun  has  a  solid  crust,  over  which  runs  the  fluid  in 
which  the  spots  are  formed.  The  current  springs  np  near 
the  poles,  and,  starting  towards  tlie  equator  without  any  rota- 
tion, is  acted  on  by  the  friction  of  the  revolving  crust.  By 
this  friction  the  crust  continually  tends  to  carry  the  fluid  with 
it.  The  nearer  the  curient  approaches  the  equator,  the  more 
rapid  the  rotation  of  the  crust,  owing  to  its  greater  distance 
from  the  axis.  The  fi-iction  acts  so  slowly  that  the  currer.t 
reaches  the  equator  before  it  takes  up  the  motion  of  the  crust. 
On  this  hypothesis,  the  crust  of  the  sun   i-eally  revolves  in 

*  Dr.  J.  C.  F.  Zollner,  Professor  in  the  University  of  Leipsio. 


THE  SUN'S  SURROUNDINGS.  257 

about  25  days ;  and  the  reason  that  the  fluid  which  covers  it 
revolves  more  slowly  at  a  distance  from  the  sun's  equator  is 
that  it  has  not  yet  taken  np  this  normal  velocity  of  rotation. 

Tliis  explanation  of  the  seeming  paradox  that  the  equatorial 
regions  of  the  sun  perform  their  revolution  in  a  shorter  tin:o 
than  those  parts  nearer  the  poles,  cannot  be  regarded  as  an  es 
tablished  scientific  theory.  It  is  mentioned  as  being,  so  far  as 
the  writer  is  aware,  the  most  completely  elaborated  explana- 
tion yet  offered.  It  is  possible  that  the  spots  have  a  proper 
motion  of  their  own  on  the  solar  surface,  and  that  this  is  the 
reason  of  the  apparent  difference  in  the  time  of  rotation  in 
different  latitudes.  Yet  another  theory  of  the  subject  is  that 
of  Faye,*  who  maintains  that  these  differences  in  the  rates  of 
rotation  are  due  to  ascending  and  descending  currents,  as  will 
be  more  fully  explained  in  presenting  his  views.  But  we  here 
touch  upon  questions  which  science  is  as  yet  far  from  being 
in  a  condition  to  answer. 

§  5.   The  Suns  Surroundings. 

If  the  sun  had  never  been  examined  with  any  other  instru- 
ment than  the  telescope,  nor  been  totally  eclipsed  by  the  inter- 
vention of  the  moon,  we  should  not  have  formed  any  idea  of 
the  nature  of  the  operations  going  on  at  his  surface  ;  but  we 
might  have  been  better  satisfied  that  we  had  a  complete  knowl- 
edge of  his  constitution.  Indeed,  it  is  remarkable  that  mod- 
ern science  has  shown  us  more  mysteries  in  the  sun  than  it  has 
explained  ;  so  that  we  find  ourselves  farther  than  before  from 
a  satisfactory  explanation  of  solar  phenomena.  When  the  an- 
cients supposed  the  sun  to  be  a  globe  of  molten  iron,  they  had 
an  explanation  which  quite  satisfied  the  requirements  of  the 
science  of  their  times.  The  spots  were  no  mystery  to  Galileo 
and  Scheiner,  being  simply  dark  places  in  the  photosphere. 
Herschel's  explanation  of  them  was  quite  in  accord  with  the 
science  of  his  time,  and  he  may  be  regarded  as  the  latest  man 
who  has  held  a  theory  of  the  physical  constitution  of  the  sun 

•  Mr.  H.  E.  Fiiye,  member  of  the  French  Academy  of  Sciences. 


258  THE  SOLAR  SYSTEM. 

which  was  really  satisfactoi-y  at  the  time  it  was  propounded 
We  have  shown  how  his  theoiy  was  refuted  by  tlie  discovery 
of  the  conservation  of  force ;  we  have  now  to  see  what  per- 
plexing phenomena  have  been  revealed  in  recent  times. 

Phenomena  during  Total  Eclipses.  —  If,  during  the  progress 
of  a  total  eclipse,  tlie  gradually  diminishing  crescent  of  the 
sun  is  watched,  nothing  remarkable  is  seen  until  very  near  the 
moment  of  its  total  disappearance.  But,  as  the  last  ray  of  sun- 
light vanishes,  a  scene  of  unexampled  beauty,  grandeur,  and  im- 
pressiveness  breaks  npon  the  view.  The  globe  of  the  moon, 
black  as  ink,  is  seen  as  if  it  were  hanging  in  mid-air,  surround- 
ed by  a  crown  of  soft,  silvery  light,  like  that  which  the  old 
painters  used  to  depict  around  the  heads  of  saints.  Besides 
this  "  corona,"  tongues  of  rose-colored  flame  of  the  most  fan- 
tastic forms  shoot  out  from  various  points  around  the  edge  of 
the  lunar  disk.  Of  these  two  appearances,  the  corona  was  no- 
ticed at  least  as  far  back  as  the  time  of  Kepler ;  indeed,  it  was 
not  possible  for  a  total  eclipse  to  happen  without  the  specta- 
tors seeing  it.  But  it  is  only  within  a  century  that  the  at- 
tention of  astronomers  has  been  directed  to  the  rose-colored 
flames,  although  an  observation  of  them  was  recorded  in  the 
Philosophical  Transactions  nearly  two  centuries  ago.  They 
are  known  by  the  several  names  of  "flames,"  "prominences," 
and  "  protuberances." 

The  descriptions  which  have  been  given  of  the  corona,  al- 
though differing  in  many  details,  have  a  general  resemblance. 
Halley's  description  of  it,  as  seen  during  the  total  eclipse  of 
1715,  is  as  follows: 

"A  few  seconds  before  the  sun  was  all  hid,  there  discovered 
itself  round  the  moon  a  luminous  ring  about  a  digit,  or  per- 
/haps  a  tenth  part  of  the  moon's  diameter,  in  breadth.  It  was 
of  a  pale  whiteness,  or  rather  pearl-color,  seeming  to  me  a  lit- 
tle tinged  with  the  colors  of  the  ii-is,  and  to  be  concentric 
with  the  moon." 

The  more  careful  and  elaborate  observations  of  recent  times 
show  that  the  corona  has  not  the  circular  form  which  was  for 
merly  ascribed  to  it,  but  that  it  is  quite  irregular  in  its  out 


THE  SUN'S  SUEBOUNDINGS.  259 

line.  Sometimes  its  form  is  more  nearly  square  than  round, 
the  corners  of  tlie  square  being  about  45°  of  solar  latitude, 
and  the  sides,  therefore,  corresponding  to  the  poles  and  the 
equator  of  tlie  sun.  This  square  appearance  does  not,  how- 
ever, arise  from  any  regularity  of  form,  but  from  the  fact  that 
the  corona  seems  brighter  and  higher  half  way  between  the 
pcles  and  the  equator  of  the  sun  than  it  does  near  those  points. 


fio.  C8. — Total  eclipse  of  the  snii  as  seen  at  Des  Moines,  Iowa,  August  Ttli,  1SC9.  Draw:; 
by  Professor  J.  R.  Eastman.  The  letters,  a,  b,  c,  etc.,  mark  the  positions  of  the  proui^ 
ineuces. 

These  prominent  portions  sometimes  seem  like  rays  shooting 
out  from  the  sun.  The  corona  is  always  brightest  at  its  base, 
gradually  shading  off  toward  the  outer  edge.  It  is  impossi- 
ble to  say  with  certainty  how  far  it  extends,  but  there  is  no 
doubt  that  it  has  been  seen  as  far  as  one  semidiameter  fror/i 
the  moon's  limb. 


260  THE  SOLAR  SYSTEM. 

The  corona  "U'as  formerly  supposed  to  be  an  atmosphere 
eitlier  of  the  moon  or  of  the  sun.  Thirty  or  forty  years  ago, 
the  most  plausible  theory  was  that  it  was  a  solar  atmosphere, 
and  that  the  red  protuberances  were  clouds  floating  in  it. 
That  the  corona  could  be  a  lunar  atmosphere  was  completely 
disproved  by  its  irregular  outline,  for  the  atmosphere  of  a 
body  like  the  ujoon  would  necessarily  spread  itself  around  in 
nearly  uniform  layers,  and  could  not  be  piled  up  in  some 
quarters,  as  the  matter  of  the  corona  is  seen  to  be.  We  shall 
soon  see  that  there  is  no  doubt  about  the  corona  being  some- 
thing surrounding  the  sun. 

The  question  whether  the  red  protuberances  belong  to  the 
moon  or  the  sun  was  settled  dui-ing  the  total  eclipse  of  1860, 
which  was  observed  in  Spain.  It  was  then  proved  by  meas- 
ures of  their  height  above  the  limb  of  the  moon  that  the  lat- 
ter did  not  carry  them  with  her,  but  passed  over  them.  This 
proved  that  they  were  flxed  relatively  to  the  sun. 

At  the  time  of  this  eclipse  the  spectroscope  was  in  its  in- 
fancy, and  no  one  thought  of  applying  it  to  the  study  of  the 
corona  and  protuberances.  The  next  considerable  eclipse  oc- 
curred eight  years  later,  in  July,  1868,  and  was  visible  in  In- 
dia and  Siam.  The  spectroscope  had,  in  the  mean  time,  come 
into  very  general  use,  and  expeditions  were  despatched  from 
several  European  couTitries  to  India  to  make  an  examination 
of  the  spectra  of  the  objects  in  question.  The  most  success- 
ful observer  was  Janssen,  of  France,  who  took  an  elevated 
position  in  the  interior,  where  the  air  was  remarkably  clear. 
When,  on  the  eventful  day,  the  last  ray  of  sunlight  was  cut 
off  by  the  advancing  moon,  an  enormous  protubei-ance  showed 
itself,  rising  to  a  height  of  manj'  thousand  miles  above  the  sur- 
face of  the  sun.  The  specti'oscope  was  promptly  turned  upon 
it,  and  the  practised  eye  of  the  observer  saw  in  a  moment  that 
the  spectrum  consisted  of  the  bright  lines  due  to  glowing  hy- 
drogen. The  protuberance,  therefore,  did  not  consist  of  any 
substance  shining  merely  by  reflected  sunlight,  but  of  an  im- 
mense mass  of  hydrogen  gas,  so  hot  as  to  shine  by  its  own 
light.  The  theory  of  the  cloud -like  nature  of  the  protuber- 
ances was  overthrown  in  a  moment. 


THE  SUN'S  SURROUNDINGS.  261 

This  observation  marks  the  commencement  of  a  new  era  in 
Solar  physics,  which,  by  a  singular  coincidence,  was  inaugu- 
i-ated  independently  by  another  observer.  As  Janssen  looked 
at  the  lines  which  he  was  the  first  of  men  to  see,  it  occurred 
to  him  that  they  were  bright  enough  to  be  seen  after  the  total 
phase  of  the  eclipse  had  passed,  lie  therefore  determined  to 
watch  them,  and  find  how  long  he  could  follow  them.  He 
kept  sight  of  them,  not  only  after  the  total  phase  had  passed, 
but  after  the  eclipse  was  entirely  over.  In  fact,  he  found  that 
with  a  sufficiently  powerful  spectroscope,  he  could  see  the 
spectral  lines  of  the  protuberances  at  any  time  when  the  air 
was  perfectly  clear,  so  that  the  varying  forms  of  these  remark- 
able objects  which  had  hitherto  been  seen  only  during  the 
rare  moments  of  a  total  eclipse  could  be  made  a  subject  of 
reorular  observation. 

But  this  great  discovery  was  made  in  England,  independ- 
ently of  the  eclipse,  by  Mr.  J.  Norman  Lockyer.  This  gen- 
tleman was  an  active  student  of  the  subject  of  spectroscopy; 
and  it  had  occurred  to  him  that  the  matter  composing  these 
protuberances,  being  so  near  the  surface  of  the  sun,  must  be 
hot  enough,  not  only  to  shine  by  its  own  light,  but  to  be  quite 
vaporized,  and,  if  so,  its  spectrum  might  be  seen  by  means  of 
the  spectroscope.  Finding  that  the  instrument  he  possessed 
would  show  nothing,  he  ordered  a  more  powerful  one.  But 
its  construction  was  attended  with  so  much  delay  that  it  was 
not  ready  till  Octobei-,  1868.  On  the  20th  of  that  uionth,  he 
pointed  it  upon  the  margin  of  the  sun,  and  f(umd  three  bright 
lines  in  the  spectrum,  two  of  which  belonged  to  hydrogen. 
Thus  was  realized  an  idea  which  he  had  formed  two  years  be- 
fore, but  which  he  was  prevented  from  carrying  out  b}^  tiie 
want  of  a  suitable  instrument.  Ilis  success  was  immediately 
communicated  to  the  French  Academy  of  Sciences,  the  news 
reaching  that  body  on  the  very  day  that  word  was  received 
from  Janssen,  in  India,  that  he  had  also  solved  the  same  prob- 
lem. 

Following  np  his  researches,  Mr.  Lockyer  found  that  the 
protuberances  arose  from  a  narrow  envelope  surrounding  the 


262 


THE  SOLAR   SYSTEM. 


i'lG.  O'.i.  — S'l  <-•-:     '•--     ;-...,         .via  [ices,  as  drawji  b_v  Secchi.     Tlie  li:ij:lu  base  ill  each 
flgnie  represents  the  chromosphere  from  which  the  red  flames  rise. 

whole  surface  of  tlie  snii,  being,  in  fact,  merely  elevated  por- 
tions of  this  envelope:  that  is  to  say,  the  sun  is  snn'onnded 
by  an  atmosphere  composed  pi-incipally  of  hydrogen  gas,  por- 
tions of  Avhieh  are  here  and  there  thrown  up  in  the  form  of 


THE  SUN'S  SURROUNDINGS.  263 

eiionnons  tongues  of  flain-e,  whicli,  however,  can  never  bo  seen 
e.\ce[)t  with  the  spectroscope,  or  during  total  eclipses.  To  this 
atmosphere  Mr.  Lockyer  gave  the  name  of  the  c/u-oniosjjhere. 

This  new  method  of  I'esearch  thi-ows  no  light  upon  tlie  con- 
stitution of  the  coi'ona,  because  the  spectrum  of  this  object  is 
too  faint  to  be  studied  at  any  time,  except  during  total  eclipses. 
There  have  been  two  in  the  United  States  within  ten  yeai's, 
during  both  of  which  the  corona  was  carefully  studied  with 
all  the  appliances  of  modern  science.  The  first  of  these 
eclipses  occurred  on  August  7th,  1869,  when  the  shadow  of 
the  moon  passed  over  Iowa,  Illinois,  Kentucky,  Sonth-western 
Virginia,  and  North  Carolina.  The  second  was  that  of  July 
29th,  1ST8,  when  the  sliadow  passed  over  Wyoming,  Colora- 
do, and  Texas.  One  of  the  most  curious  results  of  the  last 
eclipse  is  derived  from  a  study  of  the  photographs  taken  by 
parties  sent  out  from  the  Naval  Observatory.  These  show 
that  the  corona  is  not  a  mass  of  foggy  or  milky  light,  as  it 
usually  appears  in  small  telescopes,  but  has  a  hairy  structure, 
like  long  tufts  of  flax.  This  structure  was  noticed  by  W.  S. 
Gilman  dtu'ing  the  eclipse  of  1869,  but  does  not  seem  to  have 
been  generally  remai'ked.  The  most  i^rominent  feature  of  the 
spectrum  of  the  corona  is  a  single  bright  line  in  the  green 
portion,  discovered  independently  by  Professors  Ilarkness  and 
Young  during  the  eclipse  of  1869.  It  has  not  lieen  identified 
in  the  spectrum  of  any  terrestrial  substance.  This  would  in- 
dicate that  the  corona  consisted  in  part  of  some  gases  un- 
known on  the  earth.  There  is  also  a  faint  continuous  spec- 
trum, in  whicli  the  dark  lines  of  the  solar  spectrum  can  be 
seen,  but  these  lines  are  much  more  prominent  during  some 
eclipses  than  during  others.  This  portion  of  the  spectrum 
nuist  be  due  to  reflected  sunlight.  It  would  seem,  therefore, 
that  the  corona  comjM'ises  a  mixture  of  gaseous  matter,  shining 
by  its  own  light,  and  particles  reflecting  the  light  of  the  sun. 

Continued  observations  of  the  spectra  of  the  various  gases 
surrounding  the  sun  show  a  much  greater  number  of  lines 
than  have  ever  been  seen  during  total  eclipses.  Mr.  Lockyer 
himself,  by  diligent  observation  extending  over  several  years. 


264  THE  SOLAR  SYSTEM. 

found  over  a  luindred.  But  the  greatest  advance  in  this  re" 
spect  was  made  by  Professor  C.  A.  Young.  In  1S71  an  astro- 
nomical expedition  was  litted  out  by  tlie  Coast  Survey,  for  the 
purpose  of  learning  by  actual  trial  whether  any  great  advan- 
tage would  be  gained  by  establishing  an  observatory  on  the 
most  elevated  point  crossed  by  the  Pacific  Pailway.  This 
point  was  Sherman.  The  spectroscopic  part  of  the  expedition 
was  intrusted  to  Professor  Yonng.  Although  there  was  a 
great  deal  of  cloudy  weather,  yet,  when  the  air  was  clear,  far 
less  light  was  reflected  from  the  sky  surrounding  the  sun  than 
at  lower  altitudes,  which  was  a  great  advantage  in  the  study 
of  the  sun's  surroundings.  Professor  Young  found  no  less 
than  273  bright  lines  which  he  was  able  to  identify  with  cer- 
tainty. The  presence  of  many  known  substances,  especially 
iron,  magnesium,  and  titanium,  is  indicated  by  these  lines; 
but  there  are  also  mauv  lines  which  are  not  known  to  pertain 
to  any  teiTestrial  substance. 

§  G.  Physical  Constitution  of  the  Sun. 

Respecting  the  physical  constitution  of  the  sun,  there  are 
some  points  which  ma\'  be  established  with  more  or  less  cer- 
tainty, but  the  subject  is,  for  the  most  part,  involved  in  doubt 
and  obscurity.  Since  the  propeities  of  matter  are  the  same 
everywhere,  the  problem  of  tlie  physical  constitution  of  the 
snn  is  solved  only  when  we  are  able  to  explain  all  solar  phe- 
nomena by  laws  of  physics  which  we  see  in  operatioji  around 
us.  The  fact  that  the  ph3'sical  laws  operative  on  the  sun  must 
be  at  least  in  agreement  with  those  in  operation  here,  is  not 
always  remembered  by  those  who  have  speculated  on  the  sub- 
ject. In  stating  what  is  probable,  and  what  is  possible,  in 
the  causes  of  solar  phenomena,  wo  shall  begin  on  the  outside, 
and  go  inwards,  because  there  is  less  doubt  about  the  opera- 
tions which  go  on  outside  the  sun  than  about  those  on  his  sur 
face  or  in  the  interior. 

As  we  approach  the  sun,  the  lirst  material  substance  we 
meet  with  is  the  corona,  rising  to  heights  of  five  or  ten,  per- 
haps even  fifteen,  minutes  above  his  surface,  that  is,  to  a  height 


PHYSICAL   CONSTITUTION  OF  THE  SUN.  265 

of  from  one  to  tliree  hundred  thousand  miles.  Of  tliis  ap- 
pendage we  may  say  with  entire  confidence  that  it  cannot  be 
an  atmospliere  in  the  sense  in  which  that  word  is  connnonly 
used,  that  is,  a  continuous  mass  of  elastic  gas  held  np  by  its 
own  elasticity.  Of  the  two  reasons  in  favor  of  this  denial,  one 
seems  to  me  almost  conclusive,  the  other  entirely  so.  They 
are  as  follows : 

1.  Gravitation  on  the  sun  is  about  27  times  as  great  as  on 
the  earth,  and  any  gas  is  there  27  times  as  he9,vy  as  here.  In 
an  atmosphere  each  stratum  is  compressed  by  the  weight  of 
all  the  strata  above  it.  The  result  is,  that  as  we  go  down  by 
successive  equal  steps,  the  density  of  the  atmosphere  increases 
in  geotnetrical  progression.  An  atmosphere  of  the  lightest 
known  gas — hydrogen — would  double  its  density  every  five  or 
ten  miles,  though  heated  to  as  high  a  temperature  as  is  likely 
to  exist  at  the  height  of  a  hundred  thousand  miles  above  the 
sun's  surface.  But  there  is  no  approximation  to  such  a  rapid 
increase  in  the  density  of  the  corona  as  we  go  downwards.  If 
we  suppose  the  corona  to  be  such  an  atmosphere,  we  must 
suppose  it  to  be  hundreds  of  times  lighter  than  hydrogen. 

2.  The  great  comet  of  1843  passed  M'ithin  three  or  four 
minutes  of  the  surface  of  the  sun,  and  therefore  directly 
through  the  midst  of  the  corona.  At  the  time  of  nearest  ap- 
proach its  velocity  was  350  miles  per  second,  and  it  went  with 
nearly  this  velocity  through  at  least  300,000  miles  of  corona, 
coming  out  without  having  suffered  any  visible  damage  or 
retardation.  To  form  an  idea  what  M'onld  have  become  of 
it  had  it  encountered  the  rarest  conceivable  atn)osphere,  we 
have  only  to  reflect  that  shooting-stars  are  instantly  and  com- 
pletely vaporized  by  the  heat  caused  by  their  encounter  with 
Dur  atmosphere  at  heights  of  from  50  to  100  miles;  that  is,  at 
a  height  where  the  atmosphere  entirely  ceases  to  reflect  the 
light  of  the  Sim.  The  velocity  of  shooting-stars  is  from  20  to 
40  miles  per  second.  Kcmembering,  now,  that  resistance  and 
heat  increase  at  least  as  the  square  of  the  velocity,  what  would 
be  the  fate  of  a  body,  or  a  collection  of  bodies  like  a  comet, 
passing  through  several  hundred  thousand  miles  of  the  rarest 


266  THE  SOLAE  SYSTEM. 

atmosphere  at  a  rate  of  over  300  miles  a  second  ?  And  how 
rare  must  such  an  atmosphere  be  when  the  comet  passes  not 
only  wit.iout  destruction,  but  without  losing  any  sensible  ve- 
locity!  Cei-tainly  so  rare  as  to  be  entirely  invisible,  and  inca- 
pable of  producing  any  physical  effect. 

What,  then,  is  the  corona  i  Probably  detached  particles 
partially  or  wholly  vaporized  by  the  intense  heat  to  which 
they  are  exposed.  A  mere  dust -particle  in  a  cubic  mile  of 
space  wonld  shine  intensely  when  exposed  to  such  a  flood  of 
light  as  the  sun  pours  out  on  every  body  in  his  neighborhood. 
The  difficult  question  which  we  meet  is,  How  are  these  parti- 
cles held  up  ?  To  this  question  only  conjectural  replies  can 
be  given.  That  the  particles  are  not  permanently  held  in  one 
position  is  shown  by  the  fact  that  the  form  of  the  corona  is 
subject  to  great  variations.  In  the  eclipse  of  1869,  Dr.  Gould 
thought  he  detected  variations  during  the  three  minutes  the 
eclipse  lasted.  The  three  conjectures  that  have  been  formed 
on  the  subject  are  : 

1.  That  the  matter  of  the  corona  is  in  what  we  may  call  a 
state  of  projection,  being  constantly  thrown  up  by  the  sun, 
■wliile  each  particle  thus  projected  falls  down  again  according 
to  the  law  of  gravitation.  The  difficulty  we  encounter  here  is 
that  we  nuist  suppose  velocities  of  projection  rising  as  high  as 
200  miles  per  second  constantly  maintained  in  everj-  region 
of  the  solar  globe. 

2.  That  the  particles  thrown  out  by  the  sun  are  held  up  a 
greater  or  less  time  by  electrical  repulsion.  "We  know  that  at- 
mospheric electricity  plays  an  active  part  in  terrestrial  mete- 
orology;  and  if  electric  action  at  the  surface  of  the  sun  is  pro- 
portional to  those  physical  and  chemical  actions  which  we 
find  to  give  rise  to  electrical  phenomena  here  on  the  earth, 
the  development  of  electricity  there  must  be  on  an  enormous 
scale. 

3.  That  the  corona  is  due  to  clouds  of  minute  meteore  cir- 
culating around  the  sun  in  the  immediate  vicinity  of  that  lu- 
minary. 

As  already  intimated,  none  of  these  explanations  is  much 


PHYSICAL   CONSTITUTION  OF  THE  SUN  267 

better  tlian  a  conjecture,  tlioiigh  it  is  quite  probable  that  the 
facts  of  the  case  are  divided  somewhere  among  them. 

Next  inside  the  corona  lies  tlie  chromosphere.  Here  we 
reach  the  true  atmosphere  of  the  sun,  rising  in  general  a  few 
seconds  above  his  surface,  but  now  and  then  projected  up- 
wards in  immense  nuisses  whicli  we  might  call  flame,  if  the 
word  were  not  entirely  inadequate  to  convey  any  conception 


Fig.  70. — The  sun,  with  its  chiomosphere  and  red  flnmes,  on  July  23d,  1871,  as  drawt  09 
Secchi.    The  figures  mark  the  flames,  IT  iu  number. 

of  the  enormous  scale  on  which  thermal  action  is  there  car- 
ried on.  What  we  call  fii'e  and  flame  are  results  of  burn- 
ing; but  the  gases  at  the  surface  of  the  sun  are  already  so 
hot  that  burning  is  not  possible.  Hydrogen  is  the  principal 
material  of  the  npper  part  of  the  chromosphere ;  but,  as  we 
descend,  we  find  the  vapors  of  a  great  number  of  metals,  in- 
cluding iron  and  magnesium.  At  the  base,  where  the  metals 
are  most  numerous,  and  the  density  the  greatest,  occurs  the 
absorption  of  the  solar  rays  which  causes  the  dark  lines  in  the 


268  THE  SOLAR  SYSTEM. 

spectrum  already  described  (p.  225).  This  seems  satisfactori- 
ly proved  by  an  observation  of  Professor  Young's  during  the 
eclipse  of  1S70,  in  Spain.  At  the  moment  of  disappearance 
of  tlie  last  rays  of  sunlight,  when  he  had  a  glimpse  of  the 
base  of  the  chromosphere,  he  saw  all  the  spectral  lines  re- 
versed; that  is,  they  were  bright  lines  on  a  dark  ground.  The 
vapors  which  absorb  certain  rays  of  the  light  which  passes 
through  them  from  the  sun  then  emitted  those  same  rays 
when  the  sunlight  was  cut  off. 

The  most  astonishing  phenomena  connected  with  the  chro- 
mosphere are  those  outbui-sts  of  its  matter  which  form  the  pro- 
tuljei-ances.  Tlie  latter  are  of  two  classes — the  cloud-like  and 
the  eruptive.  The  tirst  class  presents  the  appearance  of  clouds 
floating  in  an  atmosphere ;  but  as  no  atmosphere  dense  enough 
to  sustain  anything  can  possibly  exist  there,  we  find  the  same 
difficult}'  in  accounting  for  them  that  we  do  in  accounting  for 
the  suspension  of  the  matter  of  the  corona.  In  fact,  of  the 
three  conjectural  explanations  of  the  corona,  two  are  inadmis- 
sible if  applied  to  the  protuberances,  since  these  cloud -like 
bodies  sometimes  remain  at  rest  too  long  to  be  supposed  mo^'- 
ing:  under  the  influence  of  the  sun's  trravitation.  This  leaves 
the  electrical  explanation  as  the  only  adequate  one  yet  brought 
forward.  The  eruptive  protuberances  seem  to  be  due  to  the 
projection  of  hydrogen  and  magnesium  vapor  from  the  region 
of  the  chromosphere  with  velocities  which  sometimes  rise  to 
150  miles  a  second.  The  eruption  may  conHnue  for  hours,  or 
even  days,  the  vapor  spreading  out  into  great  masses  thousands 
of  miles  in  extent,  and  then  falling  back  on  the  chromosph.ere. 

Is  it  possible  to  present  in  language  any  adequate  idea  of 
the  scale  on  which  natural  operations  are  here  carried  on  i  If 
we  call  the  chromosphere  an  ocean  of  fire,  we  must  remember 
that  it  is  an  ocean  hotter  tlian  the  fiercest  furnace,  and  as  deep 
as  the  Atlantic  is  broad.  If  we  call  its  movements  hurricanes, 
we  must  remember  that  our  hurricanes  blow  only  about  a  hun- 
dred miles  an  hour,  while  those  of  the  chromosphere  blow  as 
far  in  a  single  second.  They  are  such  hurricanes  as,  "  coming 
down  upon  us  from  the  north,  would,  in  thirty  seconds  after 


PHYSICAL   CONSTITUTION  OF  THE  SUN.  269 

they  had  crossed  the  St.  Lawrence,  be  in  the  Gulf  of  Mexico, 
carrying  with  them  tlie  wliole  surface  of  the  continent  in  a 
mass,  not  simply  of  ruin,  but  of  glowing  vapor,  in  which  the 
vapors  arising  from  the  dissolution  of  the  materials  composing 
the  cities  of  Boston,  New  York,  and  Chicago  would  be  mixed 
in  a  single  indistinguishable  cloud."  When  we  speak  of  erup- 
tions, we  call  to  mind  Vesuvius  burying  the  surrounding  cities 
in  lava ;  but  the  solar  eruptions,  thrown  fifty  thousand  miles 
high,  woula  ingulf  the  whole  earth,  and  dissolve  every  organ- 
ized being  on  its  suiface  in  a  moment.  When  the  mediaival 
poets  sung, 

"  Dies  iia3,  dies  ilia 
Solvet  i^asclum  in  favilla," 

they  gave  rein  to  their  wildest  imagination,  without  reaching 
any  conception  of  the  magnitude  or  fierceness  of  the  tiames 
around  the  sun. 

Of  the  corona  and  chromosphere  the  telescope  ordinarily 
shows  us  nothing.  They  are  visible  only  dui-ing  total  eclipses, 
or  by  the  aid  of  the  spectroscope.  All  we  see  with  the  eye  or 
the  telescope  is  the  shining  surface  of  the  sun  called  the  pho- 
tospiiere,  on  which  the  chromosphere  i-ests.  It  is  this  which 
radiates  both  the  light  and  the  heat  which  reach  ns.  Tlie 
opinions  of  students  respecting  the  constitution  of  the  photo- 
sphere are  so  different  that  it  is  hardly  possible  to  express  any 
views  that  will  not  be  challenged  in  some  quarter.  Although 
a  contrary  opinion  is  held  by  many,  we  may  venture  to  say 
that  the  rays  of  liglit  and  heat  seem  to  come,  not  from  a 
gas,  but  from  solid  matter.  This  is  indicated  by  the  fact  that 
their  spectrum  is  continuous,  and  also  by  the  intensity  of  the 
liglit,  which  far  exceeds  any  that  a  gas  has  ever  been  made 
to  give  forth.  It  does  not  follow  from  this  that  the  photo- 
sphere is  a  continuous  solid  or  crust,  since  floating  particles  of 
solid  matter  will  shine  in  the  same  way.  The  general  opinion 
has  been  that  the  photosphere  is  of  a  cloud-like  nature ;  that 
is,  of  minute  particles  floating  in  an  atmosphere  of  heated  gases. 
That  it  is  not  continuously  solid  like  our  earth  seemed  to  be 
fully  shown  by  the  variations  and  motions  of  the  spots,  which 


270  THE  SOLAR  SYSTEM. 

have  every  appearance  of  going  on  in  a  fluid  or  gas.  Indeed, 
of  late,  some  of  the  most  eminent  physicists  regard  it  as  pure- 
ly oraseons,  tlie  pressure  making  it  shine  like  a  solid. 

l>iit  this  theory  is  attended  with  a  difficulty  which  has  not 
been  sufficiently  considered.  The  photosphere  is  in  striking 
contrast  to  tlie  gaseous  chromosphere,  in  being  subject  to  no 
sensible  changes  of  level.  If  it  were  gaseous,  as  supposed, 
the  solid  particles  having  no  connection  with  eacii  other,  we 
should  expect  those  violent  eruptions  which  throw  up  the  pro- 
tuberances to  carry  up  portions  of  it,  so  that  it  would  now  and 
then  pi-esent  an  irregular  and  jagged  outline,  as  the  chromo- 
sphere does.  But  the  most  refined  observations  have  never 
shown  it  to  be  subject  to  the  slightest  change  of  level,  or  devi- 
ation fiom  perfect  rotundity,  except  in  the  region  of  the  spots, 
where  its  continuity  seems  to  be  broken  by  immense  chasm- 
like  openings. 

The  serene  iunnobility  of  the  photosphere,  under  such  vio- 
lent actions  around  it  as  we  have  described,  lends  some  color 
to  the  supposition  that  it  is  a  solid  crust  which  forms  around 
the  glowing  interior  of  the  sun,  oi-,  at  least,  that  it  is  composed 
of  a  comparatively  dense  fluid  resting  upon  such  a  crust.  The 
latter  is  the  view  of  ZoUner,  who  consider  some  sort  of  an 
envelope  between  the  exterior  and  the  interior  of  the  sun  ab- 
solutely necessary  to  account  for  the  eruptive  protuberances. 
He  })laces  this  solid  envelope  three  or  four  thousand  miles  be- 
low the  surface  of  the  photosphere. 

Inside  the  photosphere  we  have  the  enormous  interior 
globe,  860,000  miles  in  diameter.  The  best-sustained  theory 
of  the  interior  is  the  startling  one  that  it  is  neither  solid  nor 
iiquid,  but  gaseous;  so  that  our  great  luminary  is  nothing 
:nore  than  an  innnense  bubble.  The  pressure  upon  the  inte- 
rior portions  of  this  mass  is  such  as  to  reduce  it  to  neai'ly  the 
density  of  a  liquid;  while  the  temperature  is  so  high  as  to 
keep  the  substances  in  a  state  which  is  between  the  liquid  and 
the  gaseous,  and  in  which  no  chemical  action  is  possible.  The 
strong  point  in  support  of  this  gaseous  theory  of  the  sun's  in- 
terior is.  that  it  is  the  only  one  which  explains  how  the  sun's 


VIEWS  OK  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.    271 

light  and  heat  are  kept  up.  IIow  it  does  this  will  be  shown 
in  treating  of  the  laws  which  govern  the  secular  changes  of 
the  universe  at  large. 

§  7.  Views  of  Distinguished  Students  of  the  Sun  on  the  Subject  of 
its  Physical  Constitution. 

The  progress  of  our  knowledge  of  the  sun  during  the  past 
ten  years  has  been  so  rapid  that  only  those  can  completely  fol- 
low it  who  make  it  the  principal  business  of  their  lives.  For 
the  same  reason^  the  views  respecting  the  sun  entertained  by 
those  who  are  engaged  in  studying  it  must  be  modified  and 
extended  from  time  to  time.  The  interest  which  necessarily 
attaches  to  the  physical  source  of  all  life  and  motion  on  our 
globe  renders  the  author  desirous  of  presenting  these  views  to 
his  readers  in  their  latest  form  ;  and,  through  the  kindness  of 
several  of  the  most  eminent  investigators  of  solar  physics  now 
living,  he  is  enabled  to  gratify  that  desire.  The  following 
statements  are  presented  in  the  language  of  their  respective 
authors,  except  that,  in  the  case  of  Messrs.  Secchi  and  Faye, 
they  are  translated  from  the  French  for  the  convenience  of 
the  English  reader.  It  will  be  noticed  that  in  some  minor 
points  they  differ  from  each  other,  as  well  as  from  those  which 
the  author  has  expressed  in  the  preceding  section.  Such  dif- 
ferences are  unavoidable  in  the  investigation  of  so  difficult  a 
subject. 

Views  of  the  Rev.  Father  Secchi. — "  For  me,  as  for  every  one 
else,  the  sun  is  an  incandescent  body,  raised  to  an  enormous 
temperature,  in  which  the  substances  known  to  our  chemists 
and  physicists,  as  well  as  several  other  substances  still  unknown, 
are  in  a  state  of  vapor,  heated  to  such  a  degree  that  its  spec- 
trum is  continuous,  either  on  account  of  the  pressure  to  which 
the  vapor  is  subjected,  or  of  its  high  temperature.  This  incan- 
descent mass  is  what  constitutes  the  photosphere.  Its  limit  is 
defined,  as  in  the  case  of  incandescent  gases  in  general,  by  the 
temperature  to  which  the  exterior  layer  is  reduced  by  its  free 
radiation  in  space,  together  with  the  force  of  gravity  exert- 
ed by  the  body.  The  photosphere  presents  itself  as  composed 
N  10 


272  THE  SOLAR  SYSTEM. 

of  small,  brilliant  granulations,  separated  by  a  dark  net-work 
These  granulations  are  only  the  summits  of  the  flames  which 
constitute  them,  and  which  rise  above  the  lower  absorbing 
layer,  which  forms  the  net- work,  as  we  shall  soon  more  clearly 
see. 

"  Above  the  photospheric  layer  lies  an  atmosphere  of  a  very 
complex  nature.  At  its  base  are  the  heavy  metallic  vapors, 
at  a  temperature  which,  being  less  elevated,  no  longer  permits 
the  emission  of  light  with  a  continuous  spectrum,  although  it 
is  sufficient  to  give  direct  spectra  with  brilliant  lines,  which 
may  be  observed,  during  total  eclipses  of  the  sun,  at  its  limb. 
This  layer  is  extremely  thin,  having  a  depth  of  only  one  or 
two  seconds  of  arc.  According  to  tlic  law  of  absorption  laid 
down  by  Kirchhoff,  these  vapors  absorb  the  rays  of  the  spec- 
trum from  the  light  of  the  photosphere  which  passes  through 
them,  thus  giving  rise  to  the  breaks  known  as  the  Fraunhofer 
dark  lines  of  the  solar  spectrum.  These  vapors  are  mixed 
with  an  enormous  quantity  of  hydrogen.  This  gas  is  present 
in  such  a  quantity  that  it  rises  considerably  above  the  other 
layer,  and  forms  an  envelope  rising  to  a  height  of  from  ten 
to  sixteen  seconds,  or  even  more,  which  constitutes  what  we 
call  the  chromosphere.  This  hydrogen  is  always  mixed  with 
another  substance,  provisionally  called  helium^  wlrrnh.  forms  the 
yellow  line  D^  of  the  spectrum  of  the  protuberances,  and  with 
another  still  rarer  substance,  which  gives  the  green  line  1474 
K.  This  last  substance  rises  to  a  much  greater  elevation  than 
tlie  liydrogen ;  but  it  is  not  so  easily  seen  in  the  full  sun  as 
the  latter.  Probably  there  is  some  other  substance  not  yet 
well  determined.  Thus,  the  substances  which  compose  this 
solar  envelope  appear  to  be  arranged  in  the  order  of  their 
density ;  but  still  without  any  well-defined  separation,  the  dif- 
fusion of  the  gases  producing  a  constant  mixture. 

'•  This  atmosphere  becomes  visible  in  total  eclipses  in  the 
form  of  the  corona.  It  is  very  difficult  to  fix  its  absolute 
height.  Tlie  eclipses  j^rove  that  it  may  reach  to  a  height 
equal  to  the  solar  diameter  in  its  highest  portions. 

"  No  doubt  it  extends  yet  farther,  and  it  may  well  be  con- 


VIEWS  ON  THE  PHYSICAL  COXSTIIUTION  OF  THE  SUX.    273 

nected  Avitli  the  zodiacal  liglit.  The  visible  layer  of  this  at- 
mosphere is  not  spherical ;  it  is  higher  in  middle  latitudes, 
near  forty-live  degrees,  than  at  the  equator.  It  is  still  more 
depressed  at  the  poles.  At  the  base  of  the  chromospherej 
the  hydrogen  has  the  shape  of  small  flames  composed  of  very 
thin,  close  iilaments  Avhich  seeni  to  correspond  to  the  granu- 
lations of  the  photosphere.  During  periods  of  tranquillity 
the  direction  of  these  fllaments  is  perpendicular  to  the  solar 
surface ;  but  during  periods  of  agitation  they  are  generally 
more  or  less  inclined,  and  often  directed  systematically  tow- 
ards the  poles. 

"The  body  of  the  sun  is  never  in  a  state  of  absolute  repose. 
The  various  substances  coming  together  in  the  interior  of  the 
body  tend  to  combine,  in  consequence  of  their  affinity,  and 
necessarily  produce  agitations  and  interior  movements  of  every 
kind  and  of  great  intensity.  Hence  the  numerous  crises  which 
show  themselves  at  the  surface  through  the  elevation  of  the 
lower  strata  of  the  atmosphere  by  eruptions,  and  often  by  act- 
ual explosions.  Then  the  lower  metallic  vapors  are  projected 
to  considerable  heights,  hydi'ogen  especially,  at  an  elevation 
visible  in  the  spectroscope  (in  full  sunlight)  of  one-fourth  the 
solar  diametei'.  These  masses  of  hydrogen,  leaving  the  pho- 
tosphere at  a  temperature  higher  than  that  of  the  atmosphere, 
rise  to  the  superior  regions  of  the  latter,  remaining  suspend- 
ed, diffusing  themselves  at  considerable  elevations,  and  form- 
ing what  are  called  the  prominences  or  protuberances.  The 
structure  of  the  hydrogenous  protuberan(;es  is  entirely  simi- 
lar to  that  of  fluid  veins  raising  themselves  from  denser  layere, 
and  diffusing  in  the  more  rare  ones :  but  their  extreme  vaiia- 
bility,  even  at  the  base,  and  the  rapid  changes  of  the  place  of 
exit  and  diffusion,  prove  that  they  do  not  pass  through  any 
oriflce  in  a  solid  resisting  layer. 

"  These  eruptions  are  often  mixed  with  columns  of  metallic 
vapors  of  greater  density,  which  do  not  attain  the  elevation 
of  the  hydrogen,  and  of  which  the  nature  can  be  recognized 
by  the  aid  of  the  spectroscope :  occasionally  we  see  them  fall- 
ing back  on  the  sun  in  the  form  of  parabolic  jets.     The  most 


274  THE  SOLAR  SYSTEM. 

common  substances  are  sodium,  magnesium,  iron,  calcium,  etc. 
— indeed,  the  same  substances  which  are  seen  to  form  the  low, 
absorbing  layer  of  the  solar  atmosphere,  and  which  by  their 
absorptiou  produce  the  Fi-aunhofer  lines.  A  rigorous  and  in- 
evitable consequence  of  these  conditions  is  the  fact  that  when 
the  mass  thus  elevated  is  carried  by  the  rotation  of  the  sun 
between  the  photosphere  and  the  eye  of  the  observer,  the  ab- 
sorption becomes  very  sensible,  and  produces  a  dark  spot  on 
the  photosphere  itself.  The  metallic  absorption  lines  are 
tlien  really  wider  and  more  diffused  iu  this  region ;  and  if 
the  elevated  mass  is  high  and  dense  enough,  we  can  even  see 
the  re-reversal  of  the  lines  already  reversed;  that  is  to  say, 
we  can  see  the  bright  lines  uf  the  substance  itself  on  the  back- 
ground of  the  spot.  This  often  happens  for  hydrogen,  which 
rises  to  a  great  height,  and  also  with  sodium  and  magnesium, 
which  metals  have  the  rarest  vapors.  Here,  then,  we  have  the 
origin  of  the  solar  spots.  They  are  formed  by  masses  of  ab- 
sorbing vapors  which,  brought  out  from  the  interior  of  the  sun, 
and  interposed  between  the  photosphei-e  and  the  eye  of  the  ob- 
server, prevent  a  large  })art  of  the  light  from  reaching  our  eyes. 
"  But  these  vapors  are  heavier  than  the  surrounding  mass 
into  which  they  have  been  thrown.  The}^  therefore  fall  by 
their  own  weight,  and,  tending  to  sink  into  the  photosphere, 
produce  in  it  a  sort  of  cavity  or  basin  Ulled  with  a  darker  and 
more  absorbing  mass.  Hence  the  aspect  of  a  cavity  recognized 
in  the  spots.  If  the  eruption  is  instantaneous,  or  of  very  short 
duration,  this  vaporous  mass,  fallen  back  on  the  photosphere, 
?oon  becomes  incandescent,  reheated,  and  dissolved,  and  the 
Bpot  rapidly  disappears;  but  the  intei-ior  crises  of  the  body  of 
ihe  sun  may  be  continued  a  long  time;  and  the  eruption  may 
?naintain  itself  in  the  same  place  during  two  or  more  rotations 
r-f  the  sun.  Hence  the  persistence  of  the  spots  ;  for  the  cloud 
can  contiu'-'-e  to  form  so  long  and  so  fast  as  the  photosphere 
dissolves  it,  as  happens  with  the  jets  of  vapor  fi'om  our  vol- 
canoes. The  eruptions,  when  about  to  terminate,  may  be  re- 
vived and  reproduced  several  times  near  the  same  place,  and 
give  rise  to  spots  very  variable  in  form  and  ^fosition. 


VIEWS  O.V  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.   275 

"  The  spots  are  formed  of  a  central  region,  called  the  nu- 
cleus, or  umbra,  and  uf  a  surrounding  part  h'ss  dark,  called 
the  penumbi'a.  The  latter  is  i-eally  formed  of  thin  dark  veils, 
and  of  filaments  or  currents  of  photos})heric  matter  which 
tend  to  encroach  upon  the  dark  mass.  Tiiese  currents  have 
the  form  of  tongues,  often  composed  of  globular  masses  look- 
ing like  strings  of  beads  or  willow  leaves,  and  evidently  are 
only  the  grains  of  the  photosphere  precipitating  themselves 
towards  the  centre  of  the  spot,  and  sometimes  crossing  it  like 
a  bridire. 


Fio.  71.— ninstiatlng  Secchi's  theory  of  solar  spots. 

"  In  each  spot  we  must  distinguish  three  periods  of  ex^s^ 
ence :  the  first,  of  formation ;  the  second,  of  rest ;  the  third, 
of  extinction.  In  the  first,  the  photospheric  mass  is  raised 
and  distorted  by  a  great  agitation,  often  in  the  nature  of  a 
vortex,  which  elevates  it  all  around  the  flowing  streams,  and 
forms  irregular  elevations,  either  without  penumbra  or  with  a 
very  irregular  one.  These  irregular  movements  defy  descrip- 
tion :  their  velocities  are  enormous,  and  the  asjitated  redou 


276  THE  SOLAR  SYSTEM. 

extends  itself  over  several  square  degrees ;  but  tliis  upturn- 
inw  soon  comes  to  an  end,  and  tlie  agitation  slowly  subsides, 
and  is  succeeded  by  calm.  In  the  second  period,  the  agi- 
tated and  elevated  mass  falls  back  again,  and  tends  to  com- 
bine in  masses  more  or  less  circular,  and  to  sink  by  its  weight 
into  the  surface  of  the  photosphere.  Hence  the  depressed 
form  of  the  photosphere,  resembling  a  funnel,  and  the  numer- 
ous currents  which  come  from  each  point  of  tlie  circumference 
fto  rush  upon  this  obscure  mass ;  but  at  the  same  time  the  con- 
trast between  it  and  the  substance  issuing  still  persists.  The 
spot  takes  a  nearh'  stable  and  circular  form,  a  contrast  which 
may  last  a  long  time — so  long,  in  fact,  as  the  interior  actions  of 
the  solar  globe  furnish  new  materials.  At  length,  the  latter 
ceasing,  the  eruptive  action  languishes  and  is  exhausted,  and 
the  absorbing  mass  invaded  on  all  sides  by  the  photosphere  is 
dissolved  and  absorbed,  and  the  spot  disappears. 

"  The  existence  of  these  three  phases  is  established  by  the 
comparative  study  of  the  spots  and  eruptions.  When  a  spot 
is  on  the  sun's  border  during  its  fii-st  period,  althougli  the 
dark  region  is  invisible,  its  position  is  indicated  by  eruptions 
of  metallic  vapors,  if  the  spot  be  considerable.  On  tlie  dai-k- 
est  ones  the  vapors  of  sodium,  iron,  and  magnesium  are  seen 
in  the  greatest  quantity,  and  raised  to  great  heights.  A  calm 
and  circular  spot  is  crowned  by  beautiful  faculre  and  jets  of 
hydrogen  and  metallic  vapors,  very  low,  though  quite  brilliant. 
A  spot  which  is  on  the  point  of  closing  np  has  no  metallic 
jets,  and  at  the  utmost  only  a  few  small  jets  of  hydrogen,  and 
a  more  agitated  and  elevated  chromosphere.  Besides,  obser- 
vation teaches  that  the  eruptions  in  general  accompany  the 
spots,  and  that  they  are  deficient  at  times  when  the  spots  are 
wanting.  Thus  the  solar  activity  is  measured  by  the  double 
activity  of  eruptions  and  spots  which  have  a  common  source, 
and  the  spots  are  really  only  a  secondary  phenomenon,  de- 
pending upon  the  eruptions  and  the  more  or  less  absorbing 
quality  of  the  materials  :  if  the  erupted  materials  were  not 
absorbent,  we  could  see  no  spots  at  all. 

"  The  eruptions  composed  simply  of  hydrogen  do  not  pro 


VIEWS  ON  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.    277 

dnce  spots;  thus  they  are  seen  on  all  points  of  the  disk,  while 
the  spots  are  limited  to  the  tropical  zones,  where  alone  the 
metallic  eruptions  appear.  The  eruptions  of  simple  hydrogen 
give  rise  to  tlie  facula^.  The  greater  brilliancy  of  the  faculae 
is  due  to  two  causes :  the  first  is,  the  elevation  of  the  photo- 
sphere above  the  absorbing  stratum  of  vapor  which  is  very 
thin  (only  one  or  two  seconds  of  arc,  as  we  have  before  said) ; 
this  elevated  region  thus  escapes  the  absorption  of  the  lower 
stratum,  and  appears  more  brilliant.  The  other  cause  may  be 
that  the  hydrogen,  in  coming  out,  displaces  the  absorbing 
stratum,  and,  taking  the  place  of  the  metallic  vapors,  permits 
a  better  view  of  the  light  of  the  photosphere  itself. 

"Thus,  in  conclusion,  the  spots  are  a  secondary  phenomenon, 
but,  nevertheless,  inform  us  of  the  violent  crises  which  pre- 
vail in  the  interior  of  the  radiant  globe.  The  frequency  of 
the  spots  corresponding  to  the  frequency  of  eruptions,  the  two 
phenomena,  taken  in  connection,  are  the  mark  of  solar  activ- 
ity. The  spots  occupy  the  zones  on  each  side  of  the  solar 
equator,  and  rarely  pass  beyond  the  parallel  of  thirty  degrees. 
One  or  two  seen  at  forty-five  degrees  are  exceptions.  That 
parallel  is  therefore  the  limit  of  greatest  activity  of  the  body. 
It  is  remarkable  that  the  parallels  of  thirty  degrees  divide  the 
hemispheres  into  two  sectors  of  equal  volume.  Beyond  these 
parallels  we  see  faculse,  but  not  true  spots — or,  at  most,  only 
veiled  spots  indicative  of  a  very  feeble  metallic  eruption. 

"  Such  a  fluid  mass,  in  which  the  parts  are  exposed  to  very 
different  temperatui-es,  could  not  subsist  w'ithout  an  interior 
circulation.  We  do  not  yet  know  its  laws;  but  the  following 
facts  are  well  enough  established:  the  zones  of  spots  are  not 
fixed,  but  have  a  progressive  motion  from  the  equator  towards 
the  poles.  The  spots,  arrived  at  a  certain  high  latitude,  cease 
to  appear,  but  after  some  time  reappear  at  lower  latitudes, 
and  afterwards  go  on  anew.  Between  these  phases  of  dis- 
placement there  is  commonly  a  minimum  of  spots.  During 
periods  of  activity  the  protuberances  have  a  dominant  direc- 
tion towards  the  pole,  as  also  the  flames  of  the  chromosphere. 
This  indicates  a  general  movement  of  the  photosphere  from 


2  78  THE  SOLAR  SYSTEM. 

the  equator  to  the  poles.  This  movement  is  supported  by  thfe 
displacement  of  the  zones  of  eruption  and  of  the  protuber- 
ances, -which  always  seem  to  move  towards  the  poles. 

"  Besides  this  movement  in  latitude,  the  photosphere  has 
also  a  movement  in  longitude,  which  is  greatest  at  the  equa- 
tor. Thus  the  time  of  rotation  of  the  body  is  different  upon 
different  parallels,  the  minimum  being  at  the  equator.  These 
phenomena  lead  to  the  conclusion  that  the  entire  mass  is  af- 
fected with  a  vortical  motion  which  sets  from  the  equator 
towards  the  poles,  in  a  direction  oblique  to  the  meridians. 
The  theory  of  these  movements  is  still  to  be  elaborated,  and 
is,  no  doubt,  connected  with  the  primitive  mode  in  which  the 
sun  was  formed. 

"  The  activity  of  the  body  is  subject  to  considerable  fluctu- 
ations: the  best  established  period  is  one  of  eleven  and  one- 
third  years,  but  the  activity  increases  more  rapidly  than  it  di- 
minishes— it  increases  about  four  years,  and  diminishes  about 
seven.  This  activity  is  connected  with  the  phenomena  of  ter- 
restrial magnetism,  but  we  cannot  say  in  what  way.  We  may 
suppose  a  direct  electro-magnetic  influence  of  the  sun  upon 
our  globe,  or  an  indirect  influence  due  to  the  thermal  action 
of  the  sun,  which  reacts  upon  its  magnetism.  It  is,  indeed, 
very  natural  to  suppose  that  the  ethereal  mass  whicli  fills  the 
spaces  of  our  planetary  system  may  be  greatly  altered  and 
modified  by  the  activity  of  the  central  body.  But,  whatever 
may  be  the  cause  of  these  changes  of  activity,  we  are  com- 
pletely ignorant  of  them.  The  action  of  the  planets  has  been 
proposed  as  plausible,  but  it  is  far  from  being  satisfactory. 
The  true  explanation  is  reserved  for  the  science  wliich  shall 
reveal  the  nature  of  the  connection  whicli  unites  heat  to  elec- 
tricity, to  magnetism,  and  to  the  cause  of  gravity. 

"  Of  the  interior  of  tlie  sun  we  have  no  certain  information. 
The  superficial  temperature  is  so  great,  notwithstanding  the 
continual  loss  of  heat  whicli  it  suffei-s.  tliat  we  cannot  suppose 
it  less  in  the  interior ;  and,  consequently,  no  solid  layer  can  ex- 
ist there,  except  perhaps  at  depths  where  the  pressure  due  to 
ojravity  equals  or  surpasses  the  molecular  dilatation  produced 


VIEWS  ON  TEE  PHYSICAL  CONSTITUTION  OF  THE  SUN.   279 

by  temperature.  However  it  may  be,  the  layer  accessible  to 
the  exploration  of  our  instruments  is,  no  doubt,  fluid  and  gase- 
ous, and  we  can  thus  explain  the  variations  of  the  solar  diam- 
eter established  by  certain  astronomers.  Notwithstanding  these 
small  fluctuations,  the  radiation  of  the  body  into  its  planetary 
system  is  nearly  constant  during  widely  separated  periods,  and 
especially  is  it  so  during  the  historic  period.  This  constancy 
is  due  to  several  causes :  first,  to  the  enormous  mass  of  the 
body,  which  can  be  cooled  only  very  slowly,  owing  to  its  very 
high  temperature;  second,  to  the  contraction  of  the  mass, 
which  accompanies  the  condensation  consequent  upon  the  loss 
of  heat ;  third,  to  the  emission  of  the  heat  of  dissociation  due 
to  the  production  of  chemical  actions  which  may  take  place 
in  the  total  mass. 

"  The  origin  uf  this  heat  is  to  be  found  in  the  force  of  grav- 
ity ;  for  it  is  well  proved  that  the  solar  mass,  by  contracting 
from  the  limits  of  the  planetary  system  to  its  present  volume, 
would  produce,  not  only  its  actual  temperature,  but  one  sev- 
eral times  greater.  As  to  the  absolute  value  of  this  tempera- 
ture, we  cannot  fix  it  with  certainty.  Science  not  yet  having 
determined  the  relation  which  exists  between  molecular  liv- 
ing force  (vis  viva)  and  the  intensity  of  radiation  to  a  distance 
(which  last  is  the  only  datum  given  by  observation),  we  find 
ourselves  in  a  state  of  painful  uncertainty.  Nevertheless,  this 
temperature  must  be  several  million  degrees  of  our  thermom- 
eter, and  capable  of  maintaining  all  known  substances  in  a 
state  of  vapor, 

"  Rome,  February  11th,  1877." 

Views  of  M.  Faye. — "  In  studying  without  any  prepossession 
the  movements  of  the  spots,  we  find,  with  Mr.  Carrington,  that 
there  exists  a  simple  relation  between  their  latitude  and  their 
angular  velocity.  Nevertheless,  this  law  does  not  suffice  to 
represent  the  observations  with  the  exactitude  which  they  ad- 
mit of.  It  is  still  necessary  to  take  account  by  calculation  of  a 
parallax  of  depth  which  I  estimate  at  ^q-  of  the  radius  of  the 
sun,  and  of  certain  oscillations  of  ver}'  small  extent,  and  of 
long  period,  which  the  spots  undergo  perpendicular  to  their 


280  THE  SOLAR  SYSTEM. 

parallels.  Then  the  observations  are  represented  with  great 
precision,  from  which  I  conclude  that  we  have  to  deal  with  a 
quite  simple  mechanical  phenomenon.  The  law  in  question 
can  be  expressed  by  the  formula, 

io  =  a  —  b  sin^  X ; 
tj  being  the  angular  velocity  of  a  spot  at  the  latitude  X,  and  a 
and  b  being  constants,  having  the  same  value  (a  =  857'.6  and 
5  =  157'.3)  over  the  whole  surface  of  the  sun.  These  constants 
may  vary  slowly  with  the  time,  but  I  have  not  studied  their 
variations. 

"Admitting,  as  we  shall  see  farther  on,  that  the  velocity  of 
a  spot  is  the  same  as  the  mean  velocity  of  that  zone  of  the 
photosphere  in  which  it  is  formed,  we  see  : 

"  1.  That  the  contiguous  strips  of  the  photosphere  are  ani- 
mated with  a  velocity  of  rotation  nearly  constant  for  each  fila- 
ment, at  least  during  a  period  of  several  months  or  years,  but 
varying  with  the  latitude  from  one  strip  to  another. 

"  2.  That  these  strips  move  nearly  parallel  to  the  equator, 
and  never  give  indications  of  currents  constantly  directed  tow- 
ards either  pole,  as  in  the  upper  regions  of  our  atmosphere. 

"  3.  That  the  spots  are  hollow,  or  at  least  that  the  black  nu- 
cleus is  perceptibly  depressed  in  respect  to  the  photosphere. 

"  The  diminution  in  tlie  rate  of  superficial  rotation,  more 
tmd  more  marked  towards  the  poles,  and  the  absence  of  all 
motion  from  the  equator,  can  only  proceed  from  the  vertical 
ascent  of  materials  rising  incessantly  from  a  great  depth  tow- 
ards all  points  of  the  surface.  It  is  sufficient  that  tliis  depth 
goes  on  increasing  from  the  equator  towards  the  poles,  follow- 
ing a  law  analogous  to  tliat  of  the  rotation,  in  order  that  it 
may  produce  at  the  surface  a  retardation  increasing  with  the 
latitude.  This  retardation  is  about  two  days  in  each  rotation 
at  forty-five  degrees  of  latitude.  Tlie  mass  of  the  sun,  being 
formed  principally  of  metallic  vapoi^s  condensable  at  a  certain 
temperature,  and  that  temperature  being  reached  at  a  certain 
level  in  consequence  of  the  exterior  cooling,  there  ought  to  be 
established  a  double  vertical  movement  of  ascending  vapors, 
which  go  to  form  a  cloud  of  condensed  matter  susceptible  of 


VIEWS  ON  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.    281 

intense  radiation,  and  of  condensed  products  which  fall  back 
in  the  form  of  rain  into  the  interior.  The  latter  are  stopped 
at  the  depth  at  which  they  meet  a  temperatiii-e  high  enough 
to  vaporize  tliem  anew,  and  afterwards  force  them  to  reascend„ 
As  almost  the  entire  mass  of  the  sun  partakes  of  this  double 
movement,  the  heat  radiated  by  the  cloud  will  be  borrowed 
from  this  mass,  and  not  from  a  superficial  layer,  the  tempera- 
ture of  wliich  would  rapidly  fall,  and  which  would  soon  con- 
dense into  a  complete  crust.  Hence  the  formation  and  sup- 
port of  the  photosphere,  and  the  constancy  and  long  duration 
of  its  radiation,  which  is  also  partly  fed  by  the  slow  contrac- 
tion of  the  whole  mass  of  the  sun. 

"  The  contiguous  bands  of  the  photosphere  being  animated 
with  different  velocities,  there  results  a  multitude  of  circular 
gyratory  movements  around  a  vertical  axis  extending  to  a 
great  depth,  as  in  our  rivers  and  in  the  great  upper  currents 
of  our  atmosphere.  These  whirlpools,  which  tend  to  equalize 
the  differences  of  velocity  just  spoken  of,  follow  the  currents 
of  the  photosphere  in  the  same  way  that  whirlpools,  and  the 
whirlwinds,  tornadoes,  and  cyclones  of  our  atmosphere  follow 
the  upper  currents  in  which  tliey  originate.  Like  these,  they 
are  descending,  as  I  have  proved  (against  the  meteorologists) 
by  a  special  study  of  these  terrestrial  phenomena.  They  carry 
down  into  the  deptlis  of  the  solar  mass  the  cooler  materials  of 
the  upper  layers,  foi'med  principally  of  hydrogen,  and  thus 
produce  in  their  centre  a  decided  extinction  of  light  and  heat 
as  long  as  the  gyratory  movement  contimies.  Finally,  the 
hydrogen  set  free  at  the  base  of  the  whirlpool  becomes  re- 
heated at  this  great  depth,  and  rises  up  tumultnously  around 
the  whirlpool,  forming  irregular  jets  which  appear  above  tlie 
chromosphere.     These  jets  constitute  the  protuberances. 

"The  whirlpools  of  the  sun,  Hke  those  on  the  earth,  are  of 
all  dimensions,  from  the  scared}'  visible  pores  to  the  enormous 
spots  which  we  see  from  time  to  time.  Thej^  have,  like  those 
of  the  earth,  a  marked  tendency  first  to  increase,  and  then  to 
break  up,  and  thus  form  a  row  of  spots  extending  along  the 
same  parallel.    The  penumbra  is  due  to  a  portion  of  the  photo 


282  THE  SOLAR  SYSTEM. 

sphere  which  forms  around  their  conical  sui'face  at  a  lowei 
level,  on  account  of  the  lowering  of  the  temperature  produced 
by  the  wliirlpool.  Sometimes  in  this  sort  of  luminous  sheath  we 
see  traces  of  the  wliirling  movement  going  on  in  tlie  interior, 

"  It  is  more  difficult  to  account  for  the  periodicity  of  the 
spots.  It  seems  to  me  that  it  must  depend  upon  fluctuations  in 
the  form  of  the  interior  layer,  to  which  the  condensed  matter 
of  the  photosphere  falls  in  the  form  of  rain.  This  flow  of 
materials  from  above  must  alter,  little  by  little,  the  velocity 
of  rotation  of  this  layer.  If  its  compression  is  changed  in  the 
course  of  time,  aud  if  it  becomes  rounder,  the  variations  in 
the  superficial  velocity  of  the  photosphere,  as  well  as  the  gyra- 
tory movements,  will  diuiinish  in  intensity  and  frequency. 

"A  time  will  at  length  arrive  when  the  vertical  movements 
which  feed  the  photosphere  will  become  more  aud  more  hin- 
dered. The  cooling  will  then  be  purely  superficial,  aud  the 
surface  of  the  sun  will  harden  into  a  continuous  crust. 

"  Paris,  Februaiy,  1877.' 

Views  of  Professor  Young. — "  1.  It  seems  to  me  almost  dem- 
onstrated, as  a  consequence  of  the  low  mean  density  of  the 
sun  and  its  great  force  of  gravity,  tiiat  the  central  portions  of 
that  body,  and,  in  fact,  all  but  a  comparatively  thin  shell  near 
the  surface,  must  be  in  a  gaseous  condition,  and  the  gases  at 
so  high  a  temperature  as  to  remain  for  the  most  part  dissoci- 
ated from  each  other,  and  incapable  of  chemical  inteiaction. 
Under  the  influence  of  the  great  pressure  aud  high  teuipera- 
ture,  liowever,  their  density  and  viscosity  are  probably  such  as 
to  render  their  mechanical  behavior  more  like  that  of  such 
substances  as  tar  or  honey  than  that  of  air,  as  Ave  are  famil- 
iar with  it. 

"2.  The  visible  surface  of  the  sun,  the  photosphere,  is  com- 
posed of  clouds  formed  by  the  condensation  and  combination 
of  such  of  the  solar  gases  as  are  cooled  sufficiently  by  their 
radiation  into  space.  These  clouds  are  suspended  in  the  mass 
of  uncoudensed  gases  like  the  clouds  in  our  own  atmosphere, 
and  probably  have,  for  the  most  part,  the  forui  of  a]^proximate- 
ly  vertical  columns,  of  irregular  cross -section,  aud  a  length 


VIEWS  ON  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.  283 

many  times  exceeding  their  diameter.  The  liquid  and  solid 
particles  of  Avhich  they  are  made  up  descend  continually,  their 
places  being  constantly  supplied  by  fresh  condensation  from 
the  ascending  currents  which  rise  between  the  cloud-columns. 
From  the  under-surface  of  the  photosphere  there  must  be  an 
immense  precipitation  of  what  may  be  called  solar  'rain  and 
snow,'  which  descends  info  the  gaseous  core,  and  by  the  inter- 
nal heat  is  re-evaporated,  decomposed,  and  restored  to  its  origi- 
nal gaseous  condition ;  the  heat  lost  by  the  surface  radiation 
being  replaced  mainly  by  the  mechanical  work  due  to  the 
gradual  diminution  of  the  sun's  bulk,  and  the  thickening  of 
tlie  photosphere.  I  do  not  know  any  means  of  determining 
the  thickness  of  the  photospheric  shell,  but,  from  the  phenom- 
ena of  the  spots,  judge  that  it  can  hardly  be  less  than  ten 
thousand  miles,  and  that  it  may  be  much  more. 

"  3.  The  weight  of  the  cloud^shell,  and  the  resistance  offered 
to  the  descending  products  of  condensation,  act  to  produce  on 
the  enclosed  gaseous  core  a  constricting  pressure,  which  forces 
the  gases  upwards  through  the  intervals  between  the  clouds 
with  great  velocity ;  so  that  jets  or  blasts  of  heated  gas  con- 
tinually ascend  all  over  the  sun's  surface,  the  same  material 
subsequently  redescending  in  the  cloud-columns,  partly  con- 
densed into  solid  or  liquid  particles,  and  partly  uncondensed, 
but  greatly  cooled.  It  seems  also  not  unlikely  that  in  the  up- 
per part  of  the  channels  through  which  the  ascending  currents 
rush,  there  may  often  occur  the  mixture  of  different  gases 
cooled  by  expansion  to  temperatures  sufficiently  below  the 
dissociation  point  to  allow  of  their  explosive  combination. 

''  4.  The  '  chromosphere 'is  simply  the  layer  of  uncondensed 
gases  which  overlies  the  photosphere,  though  separated  from 
it  by  no  definite  surface.  The  lower  portion  of  the  chromo- 
sphere is  rich  in  all  the  vapors  and  gases  which  enter  into  the 
sun's  composition ;  but  at  a  comparatively  small  height  the 
denser  and  less  permanent  gases  disappear,  leaving  in  the  up- 
per regions  only  hydrogen  and  some  other  substances  not  as 
yet  identified.  The  dark  lines  of  the  solar  spectrum  originate 
mainly  in  the  absorption  produced  by  the  denser  gases  which 


2S4  THE  SOLAR   SYSTEM. 

bathe  the  photospheric  clouds,  and  these  metallic  vapoi's  are 
only  occasionally  carried  into  the  upper  regions  by  ascending 
jets  of  unusual  violence.  When  this  occurs,  it  is  almost  in- 
variably in  connection  with  a  solar  spot.  The  prominences 
are  merely  heated  masses  of  tlie  liydrogen  and  otlier  chromo- 
spheric  gases,  carried  to  a  considerable  height  by  the  ascend- 
ing currents,  and  apparently  floating  in  the  '  coronal  atmos- 
phere,' which  interpenetrates  and  overtops  the  chromosphei*e. 

"  5.  I  do  not  know  what  to  make  of  the  corona.  Its  spec- 
trum proves  that  a  considerable  portion  of  its  light  comes 
from  some  exceedingly  i-are  form  of  gaseous  matter,  which 
cannot  be  identified  with  anything  known  to  terrestrial  chem- 
istrv:  and  this  ijas,  whatever  it  inav  be,  exists  at  a  heit'ht  of 
not  less  than  a  million  of  miles  above  the  solar  suiface,  con- 
stituting the  'coronal  atmosphere.'  Another  portion  of  its 
light  appears  to  be  simply  reflected  sunshine.  But  by  what 
forces  the  peculiar  radiated  structure  of  the  corona  is  deter- 
mined.! have  no  definite  idea.  The  analogies  of  comets'  tails 
and  auroral  streamers  both  appear  suggestive;  but, on  the  other 
hand,  the  s^>ecti-a  of  the  corona,  the  aurora  borealis,  the  com- 
ets, and  the  nebulse  are  all  different — no  two  in  the  least  alike. 

"'  6.  As  to  sun-spots,  there  can  be  no  longer  any  doubt,  I 
think,  that  they  are  cavities  in  the  upper  surface  of  the  photo- 
sphere, and  that  their  darkness  is  due  simply  to  the  absorbing 
action  of  the  gases  and  vapors  which  fill  them.  It  is  also  cer- 
tain that  very  commonly,  if  not  invariably,  there  is  a  violent 
uprush  of  hydrogen  and  metallic  vapors  all  around  the  outer 
edge  of  the  penumbra,  and  a  considerable  depression  of  the 
chromosphere  over  the  centre  of  the  spot ;  probably,  also,  there 
:3  a  descending  current  through  its  centre.  As  to  the  cause 
:>f  the  spots,  and  the  interpretation  of  their  telescopic  details, 
I  an\  unsatisfied.  The  theory  of  Faye  appears  to  me,  on  the 
whole,  the  most  reasonable  of  all  that  have  yet  been  proposed; 
but  I  cannot  reconcile  it  with  the  want  of  systematic  rotation 
in  the  spots,  or  their  peculiar  forms.  Still,  it  undoubtedly  has 
important  elements  of  truth,  and  may  perhaps  be  modified  so 
as  to  meet  these  difficulties.    As  to  the  periodicity  of  the  spots, 


VIEWS  ON  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.   285 

I  am  unable  to  think  it  due  in  any  way  to  planetary  action ; 
at  least,  the  evidence  appears  to  me  wholly  insufficient  as  yet; 
but  I  have  no  hypothesis  to  offer.  Xor  have  I  any  theory  to 
propose  to  account  for  the  certain  connection  between  disturl> 
ances  of  the  solar  surface  and  of  terrestrial  magnetism. 

"  7.  As  to  the  temperature  of  the  sun's  surface,  I  have  no 
settled  opinion,  except  that  I  think  it  must  be  much  higher 
than  that  of  the  carbon  points  in  the  electric  light.  The  esti- 
mates of  those  who  base  their  calculations  on  Newton's  law  of 
cooling,  which  is  confessedly  a  mere  approximation,  seem  to 
me  manifestly  wrong  and  exaggerated  ;  on  the  other  hand,  the 
very  low  estimates  of  the  French  physicists,  who  base  their 
calculations  on  the  equation  of  Dnlong  and  Petit,  seem  to  me 
hardly  more  trustworthy,  since  their  whole  result  depends 
upon  the  accuracy  of  a  numerical  exponent  determined  by  ex- 
periment at  low  temperatures  and  under  circunistances  differ- 
ing widely  from  those  of  the  suri's  surface.  The  process  is  an 
unsafe  extrapolation.  The  sensible  constancy  of  the  solar 
radiation  seems  to  be  fairly  accounted  for  on  the  hypothesis 
of  slow  contraction  of  the  sun's  diameter. 

"  8.  I  look  upon  the  accelerated  motion  of  the  sun's  equator 
as  the  most  important  of  the  unexplained  facts  in  solar  phys- 
ics, and  am  persuaded  that  its  satisfactory  elucidation  will  carry 
with  it  the  solution  of  most  of  the  other  problems  still  pending. 

"  Such,  in  brief,  are  my  '  opinions ;'  but  many  of  them  I 
hold  with  little  confidence  and  tenacity,  and  anxiously  await 
more  light,  especially  as  regards  the  theory  of  the  sun's  rota- 
tion, the  cause  and  constitution  of  the  spots,  and  the  nature  of 
the  corona.  The  only  peculiarity  in  my  views  lies,  1  think, 
in  the  importance  I  assign  to  the  effects  of  the  descending 
products  of  condensation,  which  I  conceive  to  form  virtually 
a  sort  of  constricting  skin,  producing  pressure  upon  the  gas- 
eous mass  beneath,  something  as  the  film  of  a  bubble  com- 
presses the  enclosed  air.  To  the  pressure  thus  produced  I 
ascribe  mainly  the  eruptive  phenomena  of  the  chromosphere 
and  prominences. 

"Dartmouth  College,  March,  1877." 


286  THE  SOLAR  SYSTEM. 

Views  of  Professor  Langley. — "It  seems  to  nie  that  we  liaA'a 
now  evidence  on  which  to  pass  final  adverse  judgment  on 
views  whicli  regard  tlie  photosphere  as  an  incandescent  liqr.id, 
or  the  spots  as  analogous  either  to  scoriae  matter,  on  the  one 
hand,  or  to  clouds  above  the  luminous  surface,  on  the  other. 
According  to  direct  telescopic  evidence,  the  photosphere  is 
purely  vaporous,  and  I  consider  these  upper  vapors  to  be 
lighter  than  the  thinnest  cirri  of  our  own  sky.  The  obser- 
vation of  faculffi  allies  them  and  the  whole  'granular'  cloud 
structure  of  the  surface  most  intimately  with  chromospheric 
forms,  seen  by  the  spectroscope,  and  associates  both  Avith  the 
idea  of  an  everywhere-acting  system  of  currents  which  trans- 
mit the  internal  heat,  generated  by  condensation,  to  the  sur- 
face, and  take  back  the  cold,  absorbent  matter.  This  vertical 
circulation  goes  to  a  depth,  I  think,  sensible  even  by  compari- 
son with  the  solar  diameter.  It  coexists  with  approximately 
horizontal  movements  observed  in  what  may  be  called  the 
successive  upper  photospheric  strata  in  the  vicinity  of  spots. 
The  spots  give  evidence  of  cyclonic  action  such  as  could  only 
occur  in  a  fluid.  Their  darkness  is  due  to  the  presence,  in 
unusual  depth,  of  the  same  obscuring  atmosphere  which  forms 
the  gray  medium  in  whicli  the  luminous  photospheric  forms 
seem  suspended,  and  which  we  here  look  through,  where  it 
fills  openings  in  the  photospheric  stratum,  down  to  regions 
of  the  solar  interior  made  visible  by  the  dim  light  of  clouds 
of  luminous  vapor,  precipitated  in  lower  strata  where  the  dew- 
point  has  been  altered  by  changed  conditions  of  temperature 
and  pressure.  All  observation  and  all  legitimate  inference 
go  to  show  that  the  sun  is  gaseous  throughout  its  mass,  though 
by  this  it  is  not  meant  to  deny  the  probable  precipitation  of 
cooling  photospheric  vapors  in  something  analogous  to  rain ; 
a  condition  perhaps  necessary  to  the  maintenance  of  the  equi- 
librium of  the  interchange  of  cold  and  heated  matter  between 
exterior  and  interior ;  nor  is  it  meant  that  the  conditions  of  a 
perfect  fluid  are  to  be  expected,  where  these  are  essentially 
modified  (if  by  no  other  cause)  by  the  viscosity  due  to  extreme 
beat.     The  temperature  of  the  sun  is,  in  my  view,  necessarily 


riEWS  ox  THE  PHYSICAL  CONSTITUTION  OF  THE  SUN.   287 

much  greater  than  that  assigned  by  the  numerous  physicists, 
who  maintain  it  to  be  comparable  with  that  obtainable  in  the 
laboratory  furnace ;  but  we  cannot  confidently  assign  any  up- 
per limit  to  it  until  physics  has  advanced  beyond  its  present 
merely  empirical  rules  connecting  emission  and  tempei-ature; 
for  this,  and  not  the  lack  of  accurate  data  from  physical 
astronomy,  is  the  source  of  nearly  all  the  obscurity  now  at- 


IPfll^Pfipin 


I'M^^^^^^^^^ 


Fio.  72.— Solar  spot,  after  Langlej-. 

tending  this  important  question.  No  theory  of  the  solar  con« 
stitution  which  is  free  from  some  objection  has  yet  been  pro- 
posed ;  but  if  the  master-key  to  the  diverse  problems  it  pre- 
sents has  not  been  found,  it  is  still  true,  I  think,  that  tlie  one 
which  unlocks  most  is  tiiat  of  M.  Faye. 

"  Of  the  potential  energy  of  the  sun,  we  may  say  that  we 
believe  it  to  be  sufficient  for  a  supply  of  the  present  heat  dur- 
ing periods  to  be  counted  by  millions  of  years.     But  what  im« 

20 


288  THE  SOLAR  SYSTEM. 

mediately  concerns  ns  is  the  constancy  of  the  rate  of  conver- 
Bion  of  this  potential  into  actual  radiant  energy,  as  we  receive 
it,  for  on  tliis  depends  the  uniformity  of  the  conditions  under 
which  we  exist.  Xow,  this  uniformity  in  turn  depends  on 
the  equality  of  the  above-mentioned  interchanges  between  the 
solar  surface  and  the  interior,  an  equality  of  whose  constancy 
we  know  nothing  save  by  limited  experience.  The  most  im- 
portant statement  with  reference  to  the  sun,  perhaps,  wliich 
we  can  make  with  certainty  is  even  a  negative  one.  It  is 
that  we  have  no  other  than  empirical  grounds,  in  the  present 
state  of  knowledge,  for  believing  in  the  uniformity  of  the 
solar  radiation  in  prehistoric  periods  and  in  the  future. 

"  The  above  remarks,  limited  as  they  are,  appear  to  me  to 
cover  nearly  all  the  points  as  to  the  sun's  physical  constitu- 
tion (outside  of  the  positive  testimony  of  the  spectroscope)  on 
which  we  are  entitled  to  speak  with  confidence,  even  at  the 
present  time." 


XEE  PLANET  MERCURY. 


289 


CHAPTER  III. 


THE  INNER  GEO  DP  OF  PLANETS. 


§  1.  The  Planet  Mercury. 

Mercury  is  the  nearest  known  planet  to  the  sun,  and  the 
smallest  of  the  eight  large  planets.  Its  mean  distance  from 
the  sun  is  40  millions  of 
miles,  and  its  diameter  about 
one-third  that  of  the  earth. 
It  was  well  known  to  the  an- 
cients, being  visible  to  the 
naked  eye  at  favorable  times, 
if  the  observer  is  not  in  too 
high  a  latitude.  The  central 
and  northern  regions  of  Eu- 
rope are  so  unfavorably  sit- 
uated for  seeing  it  that  it  is 
said  Copernicus  died  without 
ever  having  been  able  to  ob- 
tain a  view  of  it.  The  diffi- 
culty of  seeing  it  arises  from 
its  proximity  to  the  sun,  as  it  seldom  sets  more  than  an  hour 
and  a  half  after  the  sun,  or  rises  more  than  that  length  of 
time  before  it.  Hence,  when  the  evening  is  sufficiently  ad- 
vanced to  allow  it  to  be  seen,  it  is  commonly  so  near  the  hori- 
zon as  to  be  lost  in  the  vapors  which  are  seen  in  that  direction. 
Still,  by  watching  for  favorable  moments,  it  can  be  seen  sevJ 
eral  times  in  the  course  of  the  year  in  any  part  of  the  United 
States.  The  following  are  favorable  times  for  seeing  it  aftejf 
sunset : 

1892 March  30tli,  July  2,')th,  November  24th. 

1893 March  13tli,  July  8th,  November  Gth. 

1894 February  2ith,  June  22d,  October  19th. 


Fig.  73.— Orbits  of  the  four  inner  planets,  Il- 
lustrating the  eccentricity  of  those  of  Mercu- 
ry and  Mars. 


290  THE  SOLAR  SYSTEM. 

The  corresponding  times  in  subsequent  years  may  be  found 
by  subtracting  IS  days  from  the  dates  for  each  year;  that  is, 
they  will  occur  IS  days  earlier  in  1S95  than  in  189^;  IS  days 
earlier  in  1S96  than  in  1895,  and  so  on.  It  is  not  necessary 
to  look  on  the  exact  days  we  have  given,  as  the  planet  is  gen- 
erally visible  for  fifteen  or  twenty  days  at  a  time.  Each  date 
given  is  about  the  middle  of  the  period  of  visibility,  which  ex- 
tends a  week  or  ten  days  on  each  side.  The  best  time  for  look- 
ing is  in  the  evening  twilight,  abont  three-quarters  of  an  hour 
after  sunset,  the  spring  is  in  this  respect  much  more  favorable 
than  autumn. 

Aspect  of  Mercury. — Mercury  shines  with  a  brilliant  white 
light,  brighter  than  that  of  a.wj  fixed  star,  except,  perhaps, 
Sirius.  It  does  not  seem  so  bright  as  Sirius,  because  it  can 
never  be  seen  at  night  except  very  near  the  horizon.  Owing 
to  the  great  eccentricity  of  its  orbit  and  the  great  variations  of 
its  distance  from  the  earth,  its  brilliancy  varies  considerably; 
but  the  favorable  times  we  have  indicated  are  near  those  of 
greatest  brightness. 

Viewed  with  a  telescope  under  favorable  conditions.  Mer- 
cury is  seen  to  have  phases  like  the  moon.  When  beyond  the 
sun,  it  seen.s  round  and  small,  being  only  about  5"  in  diame- 
ter. When  seen  to  one  side  of  the  sun,  near  its  greatest  ap- 
parent angular  distance,  it  appears  like  a  half-moon.  When 
nearly  between  the  sun  and  earth,  its  diameter  is  between  10" 
and  12",  but  only  a  thin  crescent  is  visible.  The  manner  in 
which  these  various  phases  are  connected  with  the  position  of 
the  planet  relative  to  the  earth  and  sun  is  the  same  as  in  the 
case  of  Venus,  and  will  be  shown  in  the  next  section. 

Rotation,  Figure,  Atmosphere,  etc. — About  the  beginning  of 
the  present  century  Schroter,  the  celebrated  astronomer  of 
Lilienthal,  who  made  the  telescopic  study  of  the  planets  a 
speciality,  thought  that  at  times,  when  Mercury  presented  the 
aspect  of  a  crescent,  the  south  horn  of  this  crescent  seemed 
blunted  at  certain  intervals.  He  attributed  this  appearance  to 
the  shadow  of  a  lofty  mountain,  and  by  observing  the  times 
of  its  return  was  led  to  the  conclusion  that  the  planet  revolved 


TBANSITS  OF  MERCURY.  291 

on  its  axis  in  24  hours  5  minutes.  He  also  estimated  tiie 
heiglit  of  the  mountain  at  twelve  miles.  But  the  more  power- 
ful instruments  of  modern  times  have  not  confirmed  these 
conclusions,  and  they  are  now  considered  as  quite  doubtful,  if 
not  entirely  void  of  foundation.  That  is,  we  must  regard  the 
time  of  rotation  of  Mercury  on  its  axis,  and,  of  course,  the 
position  of  that  axis,  as  not  known  with  certainty,  but  as  per- 
liaps  very  nearly  24  hours. 

The  supposed  atmosphere  of  Mercury,  the  deviation  of  its 
body  from  a  spherical  form,  and  many  other  phenomena 
which  observers  have  described,  must  be  received  with  the 
same  scepticism.  No  deviation  from  a  spherical  form  can  be 
considered  as  proved,  the  discordance  of  the  measures  showing 
that  the  supposed  deviations  are  really  due  to  errors  of  obser- 
vation. So,  also,  the  appearances  which  many  observers  have 
attributed  to  an  atmosphere  are  all  to  be  regarded  as  optical 
illusions,  or  as  due  to  the  imperfections  of  the  telescope  made 
use  of.  From  measures  of  its  light  at  various  phases  Zollner 
has  been  led  to  the  conclusion  that  Mercury,  like  our  moon, 
is  devoid  of  any  atmosphere  sufficiently  dense  to  reflect  the 
light  of  the  sun.  If  this  doubt  and  uncertainty  seems  surpris- 
ing, it  must  be  remembered  that  the  nearness  of  this  planet  to 
the  sun  renders  it  a  very  difficult  object  to  observe  with  accu- 
racy. We  must  look  at  it  either  in  the  daytime,  when  the  air 
is  disturbed  by  the  sun's  rays,  or  in  the  early  evening,  when  the 
planet  is  very  near  the  horizon,  and  therefore  in  an  unfavorable 
situation. 

Transits  of  Mercury. — Transits  of  this  planet  across  the  face 
of  the  sun  are  much  more  frequent  than  those  of  Yenus,  the 
average  interval  between  successive  transits  being  less  than  ten 
years,  and  the  longest  interval  thirteen  years.  These  transits 
are  always  looked  upon  with  great  interest  by  astronomers,  on 
account  of  the  questions  to  which  they  have  given  rise.  From 
the  earliest  ages  in  which  it  was  known  that  Mercury  moved 
around  the  sun,  it  w^as  evident  that  it  must  sometimes  pass  be- 
tween  the  earth  and  the  sun ;  but  its  diameter  is  too  siuall  to 
admit  of  its  being  seen  in  this  position  with  the  naked  eye. 


292  THE  SOLAR  SYSTEM. 

The  first  actual  observation  of  Mercury  projected  on  the  face 
of  the  sun  was  made  by  Gassendi,  on  November  7th,  1631. 
His  mode  of  observation  was  that  ah*eady  described  for  viewing 
tlie  solar  spots,  the  image  of  the  sun  being  thrown  on  a  screen 
by  means  of  a  small  telescope.  He  came  near  missing  his  ob- 
servation, owing  to  his  having  expected  that  the  planet  would 
look  much  larger  than  it  did.  The  imperfect  telescopes  of 
that  time  surrounded  every  brilliant  object  with  a  band  of 
diffused  light  which  greatly  increased  its  apparent  magni- 
tude, so  that  Gassendi  had  no  idea  how  small  the  planet  really 
was. 

Gassendi's  observation  was  hardly  accurate  enough  to  be  of 
any  scientific  value  at  the  present  time.  It  was  not  till  1677 
that  a  really  good  observation  was  made.  Halley,  of  England, 
in  that  year  was  on  the  island  of  St.  Helena,  and,  being  pro- 
vided with  superior  instruments,  was  fortunate  enough  to  make 
a  complete  observation  of  a  transit  of  Mercury  over  the  sun 
which  occurred  on  November  7th.  We  have  already  men- 
tioned the  great  accuracy  which  he  attributed  to  his  observa- 
tion, and  the  phenomenon  of  the  black  drop  which  he  was  the 
first  to  see. 

The  following  are  the  dates  at  which  transits  of  Mercury 
will  occur  during  the  next  50  years,  with  the  Washington 
times  of  mid-transit.  The  first  5  transits  will  be  visible  in 
whole  or  in  part  in  the  Atlantic  and  Mississippi  States. 


1891,  May  9th,  9h.  12m.  p.m. 
1894,  Nov.  10th,  1  h.  28  m.  p.m. 
1907,  Nov.  Uth,  7h.  Om.  a.m. 


1914,  Nov.  7th,  6  h.  58  m.  a.m. 
1924,  May  7th,  8  h.  26  m.  p.m. 
1927,  Nov.  lOih,  0  h.  37  m.  a.m. 


§  2.  The  Sujjposed  Intra- Mercurial  Planets. 

At  the  present  time  the  greatest  interest  which  attaches  to 
transits  of  Mercury  arises  from  the  conclusion  which  Lever- 
rier  has  drawn  from  a  profound  comparison  of  transits  ob- 
served before  1848  with  the  motion  of  Mercury  as  determined 
from  the  theory  of  gravitation.  This  comparison  indicates, 
according  to  Leverrier,  that  the  perihelion  of  Mercury  moves 
more  rapidly  by  40"  a  century  than  it  ought  to  from  the  grav- 


THE  SUPPOSED  INTBA-MEBCURIAL  PLANETS.        293 

itation  of  all  the  known  planets  of  the  system.  He  accounted 
for  this  motion  by  supposing  a  group  of  small  planets  between 
Mercury  and  the  sun,  and  the  question  whether  such  planets 
exist,  therefore,  becomes  important. 

Apparent  support  to  Leverrier's  tlieory  is  given  by  the  fact 
that  various  observers  have  within  the  past  century  recorded 
the  passage  over  the  disk  of  the  sun  of  dark  bodies  which  had 
the  appearance  of  planets,  and  which  went  over  too  rapidly  or 
disappeared  too  suddenly  to  be  spots.  But  when  we  examine 
these  observations,  we  find  that  they  are  not  entitled  to  the 
slightest  confidence.  There  is  a  large  class  of  recorded  as- 
tronomical phenomena  M'hich  are  seen  only  by  unskilful  ob- 
servers, with  imperfect  instruments,  or  under  unfavorable  cir- 
cumstances. The  fact  tliat  they  are  not  seen  by  practised  ob- 
servers with  good  instruments  is  sufficient  proof  that  there  is 
something  wrong  about  them.  Now,  the  observations  of  in- 
tra-Mercurial  planets  belong  to  this  class.  Wolf  has  collected 
nineteen  observations  of  unusual  appearances  on  the  sun,  ex- 
tending from  1761  to  1865,  but,  with  two  or  three  exceptions, 
the  observers  are  almost  unknown  as  astronomers.  In  at  least 
one  of  these  cases  the  observer  did  not  profess  to  have  seen 
anything  like  a  planet,  but  only  a  cloud-like  appearance.  On 
the  other  hand,  for  fifty  years  past  the  sun  has  been  constant- 
ly and  assiduously  observed  by  such  men  as  Schwabe,  Carring- 
ton,  Secchi,  and  Spoerer,  none  of  whom  have  ever  recorded 
anything  of  the  sort.  That  planets  in  such  numbers  should 
pass  over  the  solar  disk,  and  be  seen  by  amateur  observers, 
and  yet  escape  all  these  skilled  astronomers,  is  beyond  all 
moral  probability. 

In  estimating  this  probability  we  must  remember  that  a 
real  planet  appearing  on  the  sun  would  be  far  more  likely  to 
be  recognized  by  a  practised  than  by  an  unpractised  observer, 
much  as  a  new  species  of  plant  or  animal  is  more  likely  to  be 
recognized  by  a  naturalist  than  by  one  who  is  not  such.  One 
not  accustomed  to  the  close  study  of  the  solar  spots  might 
have  some  difficulty  in  distinguishing  an  unusually  round  spot 
from  a  planet.     He  is  also  liable  to  be  deceived  in  various 


294:  THE  SOLAB  SYSTEM. 

ways.*  For  instance,  the  sun,  by  his  apparent  diurnal  motion, 
presents  different  parts  of  the  edge  of  his  disk  to  the  hori- 
zon in  the  course  of  a  day ;  he  seems,  in  fact,  in  the  north- 
ern hemisphere  to  turn  round  in  tlie  same  direction  Avith  the 
hands  of  a  watch.  Hence,  if  a  spot  is  seen  near  the  edge  of 
his  disk  it  M'ill  seem  to  be  in  motion,  though  really  at  rest 
On  the  other  ]iand,  should  an  experienced  observer  see  a  planet 
projected  on  the  sun's  face,  he  could  hardly  fail  to  recognize  it 
in  a  moment ;  and  should  any  possible  doubt  exist,  it  would  be 
removed  by  a  very  brief  scrutiny. 

The  strongest  argument  against  these  appearances  being 
planets  is,  that  the  transit  of  a  planet  in  such  a  position  could 
not  be  a  rare  phenomenon,  but  would  necessarily  repeat  itself 
at  certain  intervals,  depending  on  its  distance  from  the  sun 
and  -the  inclination  of  its  orbit.  For  instance,  supposing  an 
inclination  of  10°,  "which  is  greater  than  that  of  any  of  the 
principal  planets,  and  a  distance  from  the  sun  one-half  that 
of  Mercury,  the  planet  would  pass  over  the  face  of  the  sun, 
on  the  average,  about  once  a  year,  and  its  successive  transits 
would  occur  either  very  near  the  same  day  of  the  year,  or  on 
a  certain  day  of  the  opposite  season.  The  supposed  transits 
to  which  we  have  referred  occur  at  all  seasons,  and  if  we  sup- 
pose them  real,  we  must  suppose,  as  a  logical  consequence, 
that  the  transits  of  these  several  planets  are  repeated  many 
times  a  year,  and  yet  constantly  elude  the  scrutiny  of  all  good 
observers,  though  occasionally  seen  by  unskilled  ones.  This  is 
a  sufficient  reductio  ad  absurdura  of  the  theory  of  their  reality. 

It  is  therefore  certain  that  if  the  motion  of  the  perihelion 
of  Mercury  is  due  to  a  group  of  planets,  they  are  each  so  small 
as  to  be  invisible  in  transit  across  the  sun.    It  is,  however,  pos- 

*  Some  readers  may  recall  Butler's  sarcastic  poem  of  the  "Elephant  in  the 
Moon,"  as  iUiistrative  of  the  possibility  of  an  observer  being  deceived  by  some  pe- 
culiaiity  of  his  telescope.  In  one  instance,  about  thirty  years  since,  a  telescopic 
observation  of  something  which  we  now  know  must  have  been  flights  of  distant 
birds  over  ;he  disk  of  the  sun  was  recorded,  and  published  in  one  of  the  leading 
astronomical  journals,  as  a  wonderfid  transit  of  meteors.  The  publication  was 
probably  not  senously  intended,  the  description  being  a  close  parallel  to  that  of 
the  satirical  poet.     See  Astronomische  Nachrickten,  No.  5-i9. 


THE  PLANET  VENUS.  295 

sible  that  they  raiglit  be  seen  during  total  eclipses,  either  in- 
dividually as  small  stars,  or  in  the  aggregate  as  a  cloud-like 
mass  of  light.  During  the  total  eclipse  of  July  29th,  1878, 
Professor  J.  C.  Watson  observed  two  objects  which  he  consid- 
ered to  be  such  planets,  but  there  was  a  known  star  in  tlie 
neighborhood  of  each  object,  and  it  is  considered  by  some  as- 
tronomers that  his  observations  may  have  been  really  made  on 
these  stars.  It  is  certain  that  even  if  the  objects  seen  by  Pro- 
fessor Watson  are  intratnercurial  planets,  they  are  too  small 
to  influence  the  motion  of  Mercury.  A  mass  tln-ee  or  four 
times  that  of  the  latter  planet  is  required  to  produce  the  ob- 
served effect.  The  smaller  we  suppose  the  bodies  the  more 
numerous  they  must  be,  and  since  telescopic  observations  seem 
to  show  that  most  of  them  must  be  below  the  sixth  magni- 
tude, their  number  must  be  counted  by  thousands,  and  prob- 
ably tens  of  thousands.  Now,  the  zodiacal  light  must  arise 
from  matter  revolving  around  the  sun,  and  the  question  arises 
whether  this  matter  can  be  tliat  of  which  we  are  in  search. 
One  difficulty  is,  that  unless  Ave  suppose  the  hypothetical  group 
of  planetoids  to  move  nearly  in  the  plane  of  the  orbit  of  Mer- 
cury, they  must  change  the  node  of  that  planet  as  well  as  its 
perihelion.  But  no  motion  of  the  node  above  that  due  to  the 
action  of  the  known  planets  has  been  found.  We  thus  reach 
the  enforced  conclusion  that  if  the  motion  of  the  perihelion  is 
due  to  the  cause  assigned  by  Leverrier,  the  planetoids  which 
cause  it  must,  in  the  mean,  move  in  nearly  the  same  plane 
with  Mercury.  The  strongest  argument  against  the  existence 
of  intra-mercurial  planets  is  that  they  were  carefully  searched 
for  by  experienced  observers,  during  the  total  eclipses  of  1882 
and  1883,  without  beino;  found. 

§  3.   The  Planet  Venus. 

The  planet  Venus  is  very  nearly  the  size  of  the  eartli,  its  di- 
ameter being  only  about  300  miles  less  than  that  of  our  globe. 
Next  to  the  sun  and  moon,  it  is  the  most  brilliant  object  in 
the  heavens,  sometimes  casting  a  very  distinct  shadow.  It 
never  recedes  more  than  about  45°  from  the  sun,  and  is,  there- 
O 


296  THE  SOLAB  SYSTEM. 

fore,  seen  by  night  only  in  the  western  sky  in  the  evening,  oi 
the  eastern  sky  in  the  morning,  according  as  it  is  east  or  west 
of  the  sun.  There  is,  therefore,  seldom  any  difficulty  in  rec- 
oo-uizing  it.  When  at  its  greatest  brilliancy,  it  can  be  clearly 
seen  by  the  naked  eye  in  the  daytime,  provided  that  one  knows 
exactly  where  to  look  for  it.  It  was  known  to  the  ancients  by 
the  names  of  Hesperus  and  Phosphorus,  or  the  evening  and 
the  morning  star,  the  former  name  being  given  when  the 
planet,  being  east  of  the  sun,  was  seen  in  the  evening  after 
sunset,  and  the  latter  when,  being  to  the  west  of  the  sun,  it 
was  seen  in  the  east  before  sunrise.  It  is  said  that  before  the 
birth  of  exact  astronomy  Hesperus  and  Phosphorus  were  sup- 
posed to  be  two  different  bodies,  and  that  it  was  not  until 
their  motions  were  studied,  and  the  one  was  seen  to  emerge 
from  the  sun's  rays  soon  after  the  other  was  lost  in  them,  that 
their  identity  was  established. 

Aspect  of  Venus. — To  the  unaided  eye  Venus  presents  the 
appearance  of  a  mere  star,  distinguishable  from  other  stars 
only  by  its  intense  brilliancy.  But  when  Galileo  examined 
this  planet  with  his  telescope,  he  found  it  to  exhibit  phases 
like  those  of  the  moon.  Desiring  to  take  time  to  assure  him- 
self of  the  reality  of  his  discovery,  without  danger  of  losing 
his  claim  to  priority  through  some  one  else  in  the  mean  time 
making  it  independently,  he  published  the  following  anagram, 
in  which  it  was  concealed  : 

"Ha;c  iramatura  a  me  jam  frustra  leguntur  o.  y." 
(These  unripe  things  are  now  vainly  gathered  by  me). 

By  transposing   tlie   letters   of   this    sentence  he   afterwards 
showed  that  they  could  be  made  into  the  sentence, 

"Cynthiae  figuras  scmulatur  mater  amorum." 
(The  mother  of  the  loves  imitates  the  phases  of  Cynthia). 

That  the  disk  of  Yenus  was  not  round  was  first  noticed  by 
Galileo  in  September,  1610.  A  computation  of  its  position 
at  that  time  shows  that  it  must  have  been  a  little  gibbous, 
more  than  half  of  its  face  being  illuminated;  but  after  a 


IRE  PLANET  VENUS.  297 

few  months  it  changed  into  a  crescent.  Therefore  Galileo 
could  not  have  found  it  necessary  to  wait  long  before  explain^ 
ing  his  anagram. 

The  variations  of  the  aspect  and  apparent  magnitude  of 
Venus  are  very  great,  AVhen  beyond  the  sun,  it  is  at  a  dis- 
tance of  160  millions  of  miles,  and  presents  the  appearance 
of  a  small  round  disk  10''  in  diameter.  When  nearest  the 
earth,  it  is  only  25  millions  of  miles  distant ;  and  if  its  whole 
face  were  visible,  it  would  be  more  than  60"  in  diameter. 


#      •       # 

Pia.  74 Phases  of  Venus,  showing  apparent  figure  and  magnitnde  of  the  bright  and  dark 

portions  of  the  planet  in  various  points  of  its  orbit. 

But,  being  tlien  on  the  same  side  of  the  sun  M'ith  us,  its  dark 
liemisphere  is  turned  towards  us,  except,  perhaps,  an  extreme- 
ly tliin  crescent  of  the  illuminated  hemisphere.  Between 
these  two  positions  it  goes  through  all  the  intermediate 
phases,  the  universal  rule  of  which  is  that  the  nearer  it  is 
to  the  earth,  the  smaller  the  proportion  of  its  apparent  disk 
which  is  illuminated  ;  but  the  larger  that  disk  would  appear 
could  the  whole  of  it  be  seen.  Its  greatest  brilliancy  occurs 
between  the  time  of  its  greatest  elongation  from  the  sun  and 
its  inferior  conjunction. 

Supposed  Rotation  of  Venus. — The  earlier  telescopists  natU' 
rally  scrutinized  the  planets  very  carefully,  with  a  view  of  find- 
ing whether  there  were  any  inequalities  or  markings  on  their 
surfaces  from  w^hich  the  time  of  rotation  on  tlieir  axes  could 
be  determined.  In  April,  1667,  Cassini  saw,  or  thought  he 
Baw,  a  bright  spot  on  Yenus,  by  tracing  which  for  several  suc- 
cessive evenings  he  found  that  the  planet  revolved  in  between 
23  «,nd  24:  hours.     Sixty  years  later  Blanchini,  an  Italian  a& 


298  THE  SOLAR  SYSTEM. 

tronomer,  whose  telescope  is  shown  on  page  112,  supposed  that 
he  found  seven  spots  on  the  planet,  which  he  considered  to  be 
seas.  By  vratching  them  from  night  to  night,  he  concluded 
that  it  required  more  than  2-i  days  for  Venus  to  revolve  on 
its  axis.  This  extraordinary  result  was  criticised  by  the  sec- 
ond Cassini,  who  showed  that  Blanchini,  only  seeing  the  plan- 
et a  short  time  each  evening,  and  finding  the  spots  night  after 
night  in  nearly  the  same  position,  concluded  that  it  had  moved 
very  little  from  night  to  night ;  whereas,  in  fact,  it  had  made 
a  complete  revolution,  and  a  little  more.  At  the  end  of  24 
days  it  would  be  seen  in  its  original  position,  but  would  have 
made  25  revolutions  in  the  mean  time,  instead  of  one  only,  as 
Blanchini  supposed.  This  would  make  the  time  of  rotation 
23  hours  2|-  minutes,  while  Cassini  found  23  hours  15  minutes 
from  his  father's  observations. 

Between  17SS  and  1793  Schruter  applied  to  Yenus  a  mode 
of  observation  similar  to  that  he  used  to  find  the  rotation  of 
Mercury.  AVatching  the  sharp  horns  when  the  planet  appear- 
ed as  a  crescent,  he  thought  that  one  of  them  was  blunted  at 
certain  intervals.  Attributing  this  appearance  to  a  high  moun- 
tain, as  in  the  case  of  Mercury,  he  found  a  time  of  rotation 
of  23  hours  21  minutes. 

On  the  other  hand,  Herschel  was  never  able  to  see  any  per- 
manent markings  on  Yenus.  He  thought  he  saw  occasional 
spots,  but  they  varied  so  much  and  disappeared  so  rapidly  that 
he  could  not  gather  any  evidence  of  the  rotation  of  the  plan- 
et. He  therefore  supposed  that  Yenus  was  surrounded  by  an 
atmosphere,  and  that  whatever  markings  might  be  occasional- 
ly seen  were  due  to  clouds  or  other  varying  atmospheric  phe- 
nomena. 

In  1S12,  De  Yico,  of  Rome,  came  to  the  rescue  of  the  older 
astronomers  by  publishing  a  series  of  observations  tending  to 
show  that  he  had  rediscovered  the  markings  found  by  Blan- 
chini more  than  a  century  before.  He  deduced  for  the  time 
of  rotation  of  the  planet  23  hours  21  minutes  22  seconds. 

The  best-informed  astronomers  of  the  present  day  look  with 
suspicion  on  nearly  all  these  observations,  being  disposed  to 


THE  PLANET  VENUS.  299 

Biistain  the  view  of  Herscbcl,  tliough  on  grounds  entirely  dif 
ferent  from  those  on  which  he  founded  it.  It  is  certain  that 
there  are  plenty  of  observers  of  the  present  day,  with  instru- 
ments much  better  than  those  of  their  predecessors,  who  have 
never  been  able  to  see  any  permanent  spots.  The  close  agree- 
ment between  the  times  of  rotation  found  by  the  older  ob- 
servers is  indeed  striking,  and  might  seem  to  render  it  certain 
that  they  must  have  seen  spots  which  lasted  several  days.  It 
must  also  be  admitted  in  favor  of  these  observers  that  a  fine 
steady  atmosphere  is  as  necessary  for  such  observations  as  a 
fine  telescope,  and  it  is  possible  that  in  this  respect  the  Italian 
astronomers  may  be  better  situated  than  those  farther  north. 
But  the  circum.stance  that  the  deduced  times  of  rotation  in 
the  cases  both  of  Mercury  and  Yenus  differ  so  little  from  that 
of  the  earth  is  i^umewhat  suspicious,  because  if  the  appearance 
were  due  to  any  optical  illusion,  or  imperfection  of  the  tele- 
scope, it  might  repeat  itself  several  da^'s  in  succession,  and 
thus  give  rise  to  tlie  belief  that  the  time  of  rotation  was  near- 
ly one  day.  The  case  is  one  on  which  it  is  not  at  present  poS' 
sible  to  pronounce  an  authoritative  decision;  but  the  balance 
of  probabilities  is  largely  in  favor  of  the  view  that  the  rota- 
tation  of  Venus  on  its  axis  has  never  been  seen  or  determined 
by  any  of  the  astronomers  who  have  made  this  planet  an  ob- 
ject of  stud3^* 

Atmosphere  of  Venus. — The  appearance  of  Yenus  when  near- 
ly between  us  and  the  sun  affords  very  strong  evidence  of  the 
existence  of  an  atmosphere.  The  limb  of  the  planet  farthest 
from  the  sun  is  then  seen  to  be  illuminated,  so  that  it  appears 
as  a  complete  circle  of  light.  If  only  half  the  globe  of  the 
planet  were  illuminated  by  the  sun,  this  appearance  could 
never  present  itself,  as  it  is  impossible  for  an  observer  to  see 
more  than  half  of  a  large  sphere  at  one  view.     There  is  no 

*  The  latest  physical  observations  on  Venus  with  which  I  am  acquainted  ara 
those  of  Dr.  Vogel  at  Bothkamp,  in  Part  II.  of  the  "  Bothkamp  Observations" 
^Leipzig,  Engelmann,  1873).  The  result  to  which  these  observations  point  is  that 
the  atmosphere  of  Venus  is  filled  with  clouds  so  dense  that  the  solid  body  of  the 
planet  can  not  be  seen,  and  no  time  of  rotation  can  be  determined. 


300  THE  SOLAR  SYSTEM. 

known  waj  in  which  the  sun  can  illuminate  so  much  mora 
than  the  half  of  Venus  as  to  permit  a  complete  circle  of  light 
to  be  seen  except  by  the  refraction  of  an  atmosphere. 

The  appearance  to  "which  we  allude  was  first  noticed  by 
David  Rittenhouse,  of  Philadelphia,  while  observing  the  tran- 
sit of  Yenus  on  June  3d,  17G9.  When  Yenus  had  entered 
about  half-way  upon  the  sun's  disk,  so  as  to  cut  out  a  notch  of 
the  form  of  a  half-circle,  that  part  of  the  edge  of  the  planet 
which  was  off  the  disk  appeared  illuminated  so  that  the  out- 
line of  the  entire  planet  could  be  seen.  Though  this  appear- 
ance was  confirmed  by  other  observers,  it  seems  to  have  ex- 
cited no  attention.  But  it  was  found  by  Miidler  in  1849  that 
when  Yenus  was  near  inferior  conjunction,  the  visible  crescent 
extended  through  more  than  a  half-circle.  This  showed  that 
more  than  half  the  globe  of  Yenus  was  illuminated  by  the 
Bun,  and  Madler,  computing  the  refractive  power  of  the  atmos- 
phere which  would  be  necessary  to  produce  this  effect,  found 
that  it  would  exceed  that  of  our  own  atmosphere ;  the  hori- 
zontal refraction  being  44',  whereas  on  the  earth  it  is  only 
34'.  He  therefore  concluded  that  Yenus  was  surrounded  by 
an  atmosphere  a  little  more  dense  than  that  of  the  earth. 

The  next  important  observation  of  the  kind  was  made  by 
Professor  C.  S.  Lyman,  of  Yale  College.  In  December,  1866, 
Yenus  was  very  near  her  node  at  inferior  conjunction,  and 
passed  unusually  near  the  line  drawn  from  the  earth  to  the 
sun.  Examining  the  minute  crescent  of  the  planet  with  a 
moderate-sized  telescope,  he  found  that  he  could  see  the  entire 
circle  of  the  planet's  disk,  an  exceedingly  thin  thread  of  light 
being  stretched  round  the  side  farthest  from  the  sun.  So  far 
as  known,  this  was  the  first  time  that  the  whole  circle  of  A'enus 
had  been  seen  in  this  way  since  the  time  of  Rittenhouse.  It 
is  remarkable  that  both  observations  should  have  been  made 
by  isolated  observers  in  America. 

Notwithstanding  the  concurrent  testimony  of  Rittenhouse, 
Madler,  and  Lyman,  the  bearing  of  their  observations  on  what 
was  to  be  expected  during  the  transit  of  Yenus  in  December, 
1874,  was  entirely  overlooked.     Accordingly,  many  of  the  ob- 


THE  PLANET  VENUS.  301 

servers  were  quite  taken  by  surprise  to  find  that  when  Yen  us 
was  partly  on  and  partly  off  the  sun,  the  outline  of  that  part 
of  her  disk  outside  the  sun  could  be  distinguished  by  a  deli- 
cate line  of  light  extending  around  it.  In  some  cases  the 
time  of  internal  contact  at  egress  of  the  planet  was  missed, 
through  the  observer  mistaking  this  line  of  light  for  the  limb 
of  the  sun. 

Tiiat  so  few  of  tlie  observers  saw  this  line  of  light  during 
the  transit  of  1769  is  to  be  attributed  to  the  low  altitude  of 
the  planet  at  most  of  the  stations,  and  to  the  imperfect  char- 
acter of  many  of  the  instruments  used.  It  is  also  to  be  re- 
marked that  the  observers  of  that  time  had  an  erroneous  no- 
tion of  the  appearance  which  would  be  presented  by  an  atmos- 
phere of  Venus.  It  was  supposed  that  the  atmosphere  would 
give  the  planet  a  nebulous  border  when  on  the  sun,  caused  by 
the  partial  absorption  of  the  light  in  passing  through  it.  Cap- 
tain Cook,  at  Otaheite,  made  separate  observations  of  the 
contacts  of  the  supposed  atmosphere  and  of  tlie  planet  with 
the  limb  of  the  sun.  In  fact,  however,  it  would  not  be  possi- 
ble to  see  any  indications  of  an  atmosphere  under  such  cir- 
cumstances, for  the  reason  that  the  light  passing  through  its 
denser  portions  would  be  refracted  entirely  out  of  its  course, 
so  as  not  to  reach  an  observer  on  tlie  earth  at  all. 

The  spectroscope  shows  no  indication  that  the  atmosphere 
of  Venus  exerts  any  considerable  selective  absorption  upon 
the  light  whicli  passes  through  it.  No  new  and  well-marked 
spectral  lines  are  found  in  the  light  reflected  from  the  planet, 
nor  has  the  spectrum  been  certainly  found  to  differ  from  the 
regular  solar  spectrum,  except,  perhaps,  that  some  of  the  lines 
are  a  little  stronger.  This  would  indicate  that  the  atmosphere 
in  question  does  not  differ  in  any  remarkable  degi-ee  from  our 
own,  or,  at  least,  does  not  contain  gases  which  exert  a  power- 
ful selective  absorption  on  light. 

.  Siqyposed  Visibility  of  tlie  Dark  Hemisphere  of  Venus. — Many 
astronomers  of  high  repute  have  seen  the  dark  hemisphere  of 
Venus  slightly  illuminated,  the  planet  presenting  tlie  appear^ 
ance  known  as  "  the  old  moon  in  the  new  moon's  arms,"  which 


302  THE  SOLAR  SYSTEM. 

inaj  be  seen  on  any  clear  evening  three  or  fonr  days  after  the 
change  of  the  moon.  It  is  well  known  that  in  the  case  of 
the  moon  her  dark  hemisphere  is  thus  rendered  vistble  by  the 
light  rellected  from  the  earth.  But  in  the  case  of  Yenus, 
there  is  no  earth  or  other  body  large  enough  to  shed  so  much 
light  on  the  dark  hemisphere  as  to  make  it  visible.  There 
being  no  sufficient  external  source  of  light,  it  has  been  attrib- 
uted to  a  phosphorescence  of  the  surface  of  the  planet.  If 
the  phosphorescence  were  ahvays  visible  under  favorable  cir- 
cumstances, there  would  be  no  serious  difficulty  in  accepting 
this  exjjlanation.  But,  being  only  rarely  seen,  it  is  hard  to 
conceive  how  any  merely  occasional  cause  could  act  all  at 
once  over  the  surface  of  a  planet  the  size  of  our  globe,  so  as 
to  make  it  shine.  Indeed,  one  circumstance  makes  it  ex- 
tremely difficult  to  avoid  the  conclusion  that  the  whole  ap- 
pearance is  due  to  some  nnexplained  optical  illusion.  The 
appearance  is  nearly  always  seen  in  the  daytime  or  during 
bright  twilight — rarely  or  never  after  dark.  But  such  an  il- 
lumination would  be  far  more  easily  seen  by  night  than  by 
day,  because  during  the  day  an  appearance  easily  seen  at 
night  might  be  effaced  by  the  light  of  the  sky.  If,  then,  the 
phenomenon  is  real,  why  is  it  not  seen  when  the  circumstances 
are  such  that  it  should  be  most  conspicuously  visible  i  This 
is  a  question  to  which  no  satisfactory  answer  has  been  given, 
and  nntil  it  is  answered  we  are  justified  in  considering  the  ap- 
peai'ance  to  be  purely  optical. 

Supposed  Satellite  of  Venus. — Xo  better  illustration  of  the  er- 
rors to  which  observations  with  imperfect  instruments  are  lia- 
ble can  be  given  than  the  supposed  observations  of  a  satellite 
of  Venus,  made  when  the  telescope  was  still  in  its  infancy. 
In  1G72,  and  again  in  16S6,  Cassini  saw  a  faint  object  near 
Yenus  which  exhibited  a  phase  similar  to  that  of  the  planet 
But  he  never  saw  it  except  on  these  two  occasions.  A  similar 
object  was  reported  by  Short,  of  England,  as  seen  hy  him  on 
October  23d,  1740.  The  diameter  of  the  object  was  a  third 
of  that  of  Yenus,  and  it  exhibited  a  similar  phase.  Several 
other  observers  saw  the  same  thing  between  1760  and  1764i 


THE  PLANET  VENUS.  303 

One  astronomer  went  so  far  as  to  compute  an  orbit  from  all 
the  observations;  but  it  was  an  orbit  in  which  no  satellite  of 
Venus  could  possibly  revolve  unless  tlie  mass  of  the  planet  were 
ten  times  as  great  as  it  really  is,  A  century  has  now  elapsed 
without  the  satellite  having  been  seen,  and  the  fact  that  dur- 
ing this  century  the  planet  has  been  scrutinized  with  better 
telescopes  than  any  which  were  used  in  the  observations  re- 
ferred to  affords  abundant  proof  that  the  object  was  entirely 
mythical. 

How  the  observers  who  thought  they  saw  the  object  could 
have  been  so  deceived  it  is  impossible,  at  this  distance  ot 
time,  to  say  with  certainty.  Had  they  been  inexperienced, 
we  could  say  with  some  confidence  tliat  they  were  misled  by 
the  false  images  produced  to  some  extent  in  every  telescope 
by  the  light  reflected  from  the  cornea  of  the  eye  against  the 
nearest  surface  of  the  eye-piece,  and  thence  back  again  into 
the  eye.  Similar  images  ai-e  sometimes  produced  by  the  re- 
flection of  light  between  the  surfaces  of  the  various  lenses  of 
the  eye -piece.  Thej'^  are  well  known  to  astronomers  under 
the  name  of  "  ghosts ;"  and  one  of  the  first  things  a  young  ob- 
server must  learn  is  to  distinguish  them  from  real  objects. 
They  may  also  arise  from  a  slight  maladjustment  of  the  lenses 
of  the  eye-piece,  and  if,  proceeding  from  this  cause,  they  are 
produced  only  when  the  actual  object  is  in  the  centre  of  the 
field,  they  may,  for  the  moment,  deceive  the  most  experienced 
observer.*  If,  in  an  ordinary  achromatic  telescope,  in  which 
the  interior  curvatures  of  the  lenses  are  the  same,  the  latter 
are  not  exactly  at  the  same  distance  all  the  way  round,  a  ghost 
will  be  seen  along-side  of  every  bright  object  in  all  positions. 
It  is  probable  that  all  the  observations  alluded  to  were  the  re- 
sults of  some  sort  of  derangements  in  the  telescope,  producing 
false  images  by  reflection  from  the  glasses. 


*  One  of  the  eye-pieces  of  the  great  Washington  telescope  shows  a  beautiful 
little  satellite  along -side  the  planet  Uranus  or  Neptune  when  the  image  of  the 
planet  is  brought  exactly  in  tlie  centre  of  the  field  of  view,  but  it  disappears  as 
soon  as  the  telescope  is  moved.  The  writer  was  deceived  by  this  appearance  ofj 
two  occasions  while  scrutinizing  tiiese  planets  for  close  satellites. 

21 


304  THE  SOLAR  SYSTEM. 

§  4.  The  Earth. 

Our  earth  is  the  third  planet  in  the  order  of  distance  from 
the  snn,  and  slightly  the  largest  of  the  inner  group  of  four. 
Its  mean  distance  from  the  sun  is  about  92^  millions  of  miles; 
but  it  is  a  million  and  a  half  less  than  this  mean  on  January 
1st  of  every  year,  and  as  much  greater  on  July  1st.  That 
is,  its  actual  distance  varies  from  91  to  94  millions  of  miles. 
As  already  remarked,  these  numbers  are  uncertain  by  several 
hundred  thousand  miles. 

Much  of  what  we  may  call  the  astronomy  of  the  earth — 
such  as  its  figure  and  mass,  the  length  of  the  year,  the  obliq- 
uity of  the  ecliptic,  the  causes  of  the  changes  in  the  seasons 
and  in  the  length  of  the  days — has  already  been  treated  in 
the  chapter  on  gravitation,  so  that  we  have  little  of  a  purely 
astronomical  character  to  add  here.  The  features  of  its  sur- 
face and  the  phenomena  of  its  atmosphere  belong  rather  to 
geography  and  meteorology  than  to  astronomy.  But  its  consti- 
tution gives  rise  to  several  questions  in  the  treatment  of  which 
astronomical  considerations  come  into  play.  Prominent  among 
these  is  that  of  the  state  of  the  great  interior  mass  of  our 
globe,  whether  solid  or  liquid.  It  is  well  known  that  wher- 
ever we  descend  into  the  solid  portions  of  the  earth,  we  find  a 
rise  in  temperature,  going  on  uniformly  with  the  depth,  at  a 
rate  which  nowhere  differs  greatly  froui  1°  Fahrenheit  in  50 
feet.  This  rise  of  temperature  has  no  connection  with  the 
sea-level,  but  is  found  at  all  points  of  the  surface,  no  matter 
how  elevated  they  may  be.  Wherever  a  difference  of  temper- 
ature like  this  exists,  there  is  necessarily  a  constant  transfer  of 
heat  from  the  Avarmer  to  the  cooler  strata  by  conduction.  In 
this  way,  the  inequality  would  soon  disappear  by  the  warmer 
strata  cooling  off,  if  there  were  not  a  constant  supply  of  heat 
inside  the  earth.  The  rise  of  temperature,  therefore,  cannot 
be  something  merely  superficial,  but  must  continue  to  a  great 
depth.  If  we  trace  to  past  times  the  conditions  which  must 
have  existed  in  order  that  the  increase  might  show  itself  at  the 
present  time,  we  shall  find  it  almost  certain  that,  a  thousand 


THE  EARTH.  305 

years  ago,  the  whole  eartli  was  red-hot  at  a  distance  of  ten  oi 
fifteen  miles  below  its  surface ;  because  otherwise  its  interior 
could  not  have  furnished  the  supply  of  heat  which  now  causes 
the  observed  increase.  This  being  the  case,  it  is  probably  red- 
hot  still,  since  it  would  be  absurd  to  expect  a  state  of  things 
like  this  to  be  merely  temporary.  In  a  word,  we  have  every 
reason  to  believe  that  the  increase  of  say  100°  a  mile  contin^ 
lies  many  miles  into  the  interior  of  the  earth.  Then  we  shall 
have  a  red  heat  ut  a  distance  of  12  miles,  while,  at  the 
depth  of  100  miles,  the  temperature  will  be  so  high  as  to 
melt  most  of  the  materials  which  form  the  solid  crust  of  the 
globe. 

We  are  thus  led  to  the  theory,  very  generally  received  by 
geologists,  that  the  earth  is  really  a  sphere  of  molten  matter 
surrounded  by  a  comparatively  thin  solid  crust,  on  which  we 
live.  This  crust  floats,  as  it  were,  on  the  molten  interior.  It 
must  be  confessed  that  geological  facts  are,  on  the  whole,  fa- 
vorable to  this  view.  Observations  on  the  pendulum  have 
been  supposed  to  show  that  the  specific 
gravity  of  the  earth  under  the  great 
mountain  chains  is  generally  less  than  in 
the  adjoining  plains,  which  is  exactly  the 
result  that  would  flow  from  the  theory. 
The  heavier  masses,  pressing  upon  the  in- 
terior fluid,  would  tend  to  elevate  the  sur- 
rounding lighter  masses,  and  when  the  two  Fig. rs.-showing  thickness 
were  in  equilibrium,  the  latter  would  be     "f  the  earth's  crust  accord- 

■I-  '  ing  to  the  geological  tbeo- 

the  higher,  as  a  floating  block  of  pine  ry  of  a  moiteu  interior. 
wood  will  rise  higher  out  of  the  water  pr^opoSn  thau The  ToiiS 
than  a  block  of  oak.  Boiling  springs  in  ^rust. 
many  parts  of  the  globe  show  that  there  are  numerous  hot  re- 
gions in  the  earth's  interior,  and  this  heat  cannot  be  merely 
local,  because  then  it  would  soon  be  dissipated.  But  the  geol- 
ogist finds  the  strongest  proof  of  the  theory  in  volcanoes  and 
earthquakes.  The  torrents  of  lava  which  have  been  thrown 
out  of  the  former  through  thousands  of  years  show  that  there 
are  great  volmnes  of  molten  matter  in  the  earth's  interior. 


306  THE  SOLAR  SYSTEM. 

wliile  the  latter  show  this  interior  to  be  subject  to  violent 
changes  which  a  solid  could  not  exhibit. 

But  mathematicians  have  never  been  able  entirely  to  rec- 
oncile the  theory  in  question  with  the  observed  phenomena  of 
precession,  nutation,  and  tides.  To  all  appearance,  the  earth 
resists  the  tide-producing  action  of  the  sun  and  moon  exactly 
as  if  it  were  solid  from  centre  to  circumference.  Sir  William 
Thomson  has  shown  that  if  the  earth  were  less  rigid  than  steel, 
it  would  yield  so  much  to  this  action  that  the  tides  would  be 
mucli  smaller  than  on  a  perfectly  rigid  earth ;  that  is,  the  at- 
traction of  the  bodies  in  question  would  draw  the  earth  itself 
out  into  an  ellipsoidal  form,  instead  of  drawing  merely  the 
waters  of  the  ocean.  Earth  and  ocean  moving  together,  we 
could  see  no  tides  at  all.  If  the  earth  were  only  a  thin  shell 
floating  on  a  liquid  interior,  the  tides  would  be  produced  in 
the  latter ;  the  thin  shell  would  bend  in  such  a  way  that  the 
tides  in  the  ocean  would  be  nearly  neutralized.  Again,  the 
question  has  arisen  whether  the  liquid  interior  Avould  be  af- 
fected by  precession  ;  whether,  in  fact,  the  crust  would  not  slip 
over  it,  so  that  in  time  the  liquid  would  rotate  in  one  direc- 
tion, and  the  crust  in  another.  Altogether,  the  doctrine  of  the 
earth's  fluidity  is  so  fraught  with  difiiculty  that,  notwithstand- 
ing the  seeming  strength  of  the  evidence  in  its  favor,  it  must 
be  regarded  as  at  least  very  doubtful.  It  may  be  added  that 
no  one  denies  that  the  interior  of  our  planet  is  intensely  hot — 
hot  enough,  in  fact,  to  melt  the  rocks  at  its  surface  —  but  it 
is  supposed  that  the  enormous  pressure  of  the  outer  portions 
tends  to  keep  the  inner  part  from  melting.  Xor  is  it  ques- 
tioned by  Sir  William  Thomson  that  there  are  great  volumes 
of  melted  matter  in  the  earth's  interior  from  which  volcanoes 
are  fed ;  but  he  maintains  that,  after  all,  these  volumes  are 
smaU  compared  with  that  of  the  whole  earth. 

Refrojciion  of  the  Atmosphere. — If  a  ray  of  light  pass  through 
our  atmosphere  in  any  other  than  a  vertical  direction,  it  is 
constantly  curved  downwards  by  the  refractive  power  of  that 
medium.  The  more  nearly  horizontal  the  coui-se  of  the  ray, 
the  greater  the  curvature.      In  consequence  of  this,  all  the 


THE  EARTH.  307 

heavenly  bodies  appear  a  little  nearer  the  zenith,  or  a  little 
higher  above  the  horizon,  than  they  actually  are.  The  dis- 
placement is  too  small  to  be  seen  by  the  naked  eye  except 
quite  near  the  horizon,  where  it  increases  rapidly,  amounting 
to  more  than  half  a  degree  at  the  horizon  itself.  Consequent- 
ly, at  any  point  where  we  have  a  clear  horizon,  as  on  a  prairie, 
or  the  sea-shore,  the  whole  disk  of  the  sun  will  be  seen  above 
the  horizon  when  the  true  direction  is  below  it.  A  slight  in- 
crease is  thus  given  to  the  length  of  the  day.  The  sun  in  our 
latitudes  always  rises  three  or  four  minutes  sooner,  and  sets 
three  or  four  minutes  later,  than  he  would  if  there  were  no 
atmosphere.  At  the  time  of  tlie  equinoxes,  if  we  suppose  the 
day  to  begin  and  end  when  the  centre  of  the  sun  is  on  the 
horizon,  it  is  not  of  the  same  length  with  the  night,  but  is  six 
or  eight  minutes  longer.  If  we  suppose  the  day  to  begin  with 
the  rising  of  the  sun's  upper  limb,  and  not  to  end  till  the  same 
limb  has  set,  then  we  must  add  some  three  minutes  more  to 
its  length. 

If,  standing  on  a  hill,  we  watch  the  sun  rise  or  set  over  the 
ocean,  one  effect  of  refraction  will  be  quite  clearly  \isible. 
When  his  lower  limb  almost  seems  to  touch  the  water,  it  will 
be  seen  that  the  form  of  liis  disk  is  no  longer  round,  but  ellip- 
tical,  the  horizontal  diameter  being  greater  than  the  vertical. 
The  reason  of  this  is  that  the  lower  limb  is  more  elevated  by 
refraction  than  the  upper  one,  and  thus  the  vertical  diameter 
is  diminished. 

In  practical  astronomy,  all  observations  of  the  altitude  of 
the  heavenly  bodies  above  the  horizon  must  be  corrected  for 
refraction,  the  true  altitude  being  always  less  than  that  ob- 
served. Yery  near  the  zenith  the  refraction  is  about  1"  for 
every  degree,  or  -jJy-jj-  part  the  distance  from  the  zenith.  But 
it  increases  at  first  in  the  proportion  of  the  tangent  of  the  ze- 
nith distance,  so  that  at  45°,  or  half-way  between  the  zenith 
and  the  horizon,  it  amounts  to  60" ;  at  the  horizon  it  is  34'. 

TJie  Aurora  Borealis. —  This  phenomenon,  though  so  well 
known,  is  one  of  which  great  difficulty  has  been  found  in  giv- 
ing a  satisfactory  explanation.     That  it  is  in  some  way  con- 


308 


THE  SOLAR  SFSTEM. 


Fig.  76.— Distribntion  of  auroras,  after  Loomis.    The  darker  the  color,  the  more  frequently 

auroras  are  seen. 

nected  with  the  pole  of  the  earth  is  shown  by  the  fact  that 
its  frequency  depends  on  the  Latitude.  In  the  equatorial  re- 
gions of  our  globe  it  is  quite  rare,  and  increases  in  frequency 
as  we  go  north.     But  the  region  of  greatest  frequency  see»?as 


THE  EARTH. 


309 


to  be,  not  the  poles,  bnt  the  neigliborhood  of  the  Arctic  Cir- 
cle, from  which  it  diminishes  towards  both  the  north  and  the 
Bouth.  This  is  shown  more  exactly  in  Professor  Loomis's 
auroral  map,  of  which  we  give  a  copy  on  the  preceding  page. 
A  close  study  of  the  aurora  indicates  that  its  connection  is 
not  with  the  geographical,  but  with  the  magnetic  pole.  Two 
distinct  kinds  of  light  are  seen  in  the  aurora ;  or  we  might 
say  that  the  light  assumes  two  distinct  forms,  of  which  some- 
times the  one  and  sometimes  the  other  preponderates.  They 
are  as  follows : 

1.  The  cloud-like  form.  This  consists  of  a  large  irregular 
patch  of  light,  frequently  of  a  red  or  purple  tinge.  It  is  seen 
in  every  direction,  but  more  frequently  in  or  near  the  northern 
horizon,  where  it  assumes  the  form  of  an  arch  or  croMU  of 
light.  The  two  ends  of  the  arch  rest  on  the  horizon,  one  on 
each  side  of  the  north  point.  The  middle  of  the  arch  rises  a 
few  deo^rees  above  the  horizon. 


Fio.  77.— View  of  anroia. 


2.  The  streamer  or  pillar  form.  This  form  consists  of  long 
streamers  or  pillars,  which  extend  in  the  direction  of  the  dip- 
ping magnetic  needle.  They  look  curved  or  arched,  like  the 
celestial  sphere  on  which  they  are  projected,  but  they  are  re- 
ally straight.    They  are  in  a  state  of  constant  motion.    Some- 


310  TEE  SOLAR  SYSTEM. 

times  they  are  spread  out  in  the  form  of  an  immense  flag 
with  numerous  folds,  dancing,  quivering,  and  undulating,  as 
if  moved  by  the  wind. 

Electric  Kalure  of  the  Aurora. — There  is  abundant  evidence 
that  the  aurora  is  intimately  connected  with  the  electricity 
and  magnetism  of  the  earth.  Durinor  a  brilliant  aurora  such 
strong  and  irregular  currents  of  electricity  pass  through  the 
telegraph  wires  that  it  is  diflicult  to  send  a  despatch.  Some- 
times the  current  runs  with  such  force  that  a  message  may 
be  sent  without  a  battery.  The  magnetic  needle  is  also  in  a 
state  of  great  agitation.  Before  the  spectroscope  came  into 
use,  these  electric  phenomena  gave  rise  to  the  opinion  that 
the  aurora  was  due  entirely  to  currents  of  electricity  passing 
through  the  upper  regions  of  the  atmosphere  from  one  pole  to 
the  other.  But  recent  researches  seem  to  show  that,  though 
this  view  may  be  partly  true,  it  is  far  from  the  wliole  truth, 
and  does  not  afi^ord  a  complete  explanation.  The  great  height 
of  the  aurora  and  the  nature  of  its  spectrum  both  militate 
against  it. 

Height  of  the  Aurora. — Several  attempts  have  been  made  in 
recent  times  to  determine  the  height  of  the  aurora  above  the 
surface  of  the  earth,  by  simultaneous  observations  of  some 
prominent  streamer  or  patch  of  light  from  several  far-distant 
stations.  The  general  result  is  tliat  it  extends  to  the  height  of 
from  400  to  600  miles.  But  the  evidence  of  shooting -stars 
and  meteors  seems  to  indicate  that  the  limit  of  the  atmosphere 
is  between  100  and  110  miles  in  height.  If  it  extends  above 
this,  it  must  be  too  rare  to  conduct  electricity  long  before  it 
reaches  the  greatest  height  of  the  aurora  ;  indeed,  it  is  doubt- 
ful whether  it  does  not  attain  this  rarity  at  a  height  of  40  or 
50  miles.  If,  then,  the  aurora  really  extends  to  the  great 
height  we  have  mentioned,  and  still  exists  in  a  gaseous  medi- 
um, it  seems  difficult  to  avoid  the  conclusion  that  this  medium 
is  something  far  more  ethereal  than  the  gases  which  form  our 
atmosphere.  It  would,  however,  be  unphilosophical  to  assume 
the  existence  of  such  a  medium  without  some  other  evidence 
in  its  favor  than  that  afforded  by  the  aurora.     We  must  in- 


TEE  EARTH. 


3H 


elude  the  aurora  among  those  things  in  which  modern  ol> 
servations  have  opened  up  more  difficulties  than  modern  theo' 
ries  have  explained. 

Spectrum  of  the  Aurora. — The  spectrum  of  the  aurora  is  so 
far  fi'om  uniform  as  to  be  quite  puzzling.  There  is  one  char- 
acteristic bright  line  in  the  green  part  of  the  spectrum,  known 
as  Angstrom's  line,  from  its  lirst  discoverer.  This  was  the 
only  line  Angstrom  could  see :  he  therefore  pronounced  the 
light  of  tlie  aurora  to  be  entii-ely  of  one  color.  Subsequent 
observers,  however,  saw  many  additional  lines,  but  they  were 
different  in  different  auroras.  Among  those  who  have  made 
careful  studies  of  the  aurora  with  the  spectroscope  are  the 
late  Professor  Winlock,  of  Harvard  University;  Professor 
Barker,  of  Philadelphia ;  and  Dr.  H.  C.  Yogel,-  formerly  of 
Bothkamp. 


Fig.  "8.— Spectrum  of  two  of  the  great  auroras  of  1S71,  after  Dr.  H.  C.  VogeL 

Fig.  78  shows  the  spectra  of  two  auroras,  as  drawn  by  Dr. 
Vogel.  It  will  be  seen  that  there  is  one  fine  briglit  line  be- 
tween D  and  E,  which  would  fall  in  the  yellowish-green  part 
of  the  spectrum,  while  the  others  are  all  broad,  ill -defined 
bands.  Dr.  Yogel  notices  a  remarkable  connection  between 
tliese  lines  and  several  groups  of  lines  produced  by  the  vapor 
of  iron,  and  inquires  whether  this  vapor  can  possibly  exist  in 
the  upper  regions  of  our  atmosphere.  A  more  complete  study 
of  the  spectra  of  vapors  at  different  pressures  and  tempera- 
tures is  necessary  before  we  can  form  a  decided  opinion  as  to 
what  the  aurora  really  is. 


312 


THE  SOLAR  SYSTEM. 


Of  the  supposed  periodicity  of  the  aurora,  and  its  connection 
with  snn-spots,  we  have  ah-eady  spoken.  Granting  the  reality 
of  tliis  connection,  we  may  expect  that  auroras  will  be  very 
frequent  between  the  years  1880  and  1884;  and  if  this  ex- 
pectation is  realized,  little  doubt  of  the  connection  will  remain. 

§  5.  The  Moon. 

The  moon  is  much  the  nearest  to  us  of  all  the  heavenly 
bodies;  no  other,  except  possibly  a  comet,  ever  coming  nearer 
than  a  hundred  times  her  distance.  Her  mean  distance  is,  in 
round  numbers,  240,000  miles.  Owing  to  the  ellipticity  of  her 
orbit  and  the  attractive  force  of  the  sun,  it  varies  from  ten  to 
twenty  thousand  miles  on  each  side  of  this  mean  in  the  course 
of  each  monthly  revolution.  The  least  possible  distance  is 
221,000  miles ;  the  greatest  is  259,600  miles.  It  very  rarely 
approaches  either  of  these  limits,  the  usual  oscillation  being 
about  13,000  miles  on  each  side  of  the  mean  distance  of 
240,300.  The  diameter  of  the  moon  is  2160  miles,  or  some- 
what less  than  two-sevenths  that  of  the  earth.  Her  volume  is 
about  one-fiftieth  that  of  the  eartli,  and  if  she  were  as  dense 
as  the  latter,  her  mass   would  be  in   the   same  proportion. 


Fig.  79.— Relative  size  of  eartii  and  moon. 


But  her  actual  mass  is  only  about  one-eiglitieth  that  of  the 
earth,  showing  that  her  density,  or  the  specific  gravity  of  the 
material  of  which  she  is  composed,  is  little  more  than  half  that 


THE  MOON.  313 

of  our  globe.  Her  weight  is,  in  fact,  about  Z^  times  that  of 
her  bulk  of  water. 

The  most  remarkable  feature  of  the  motion  of  the  moon  is, 
that  she  makes  one  revolution  on  her  axis  in  the  same  time 
that  she  revolves  around  the  earth,  and  so  always  presents  the 
same  face  to  us.  In  consequence,  the  other  side  of  the  moon 
must  remain  forever  invisible  to  human  eyes.  The  reason  of 
this  peculiarity  is  to  be  found  in  the  ellipticity  of  her  globe. 
Tiiat  she  should  originally  have  been  set  in  revolution  on  her 
axis  with  precisely  the  same  velocity  with  which  she  revolved 
around  the  earth,  so  that  not  the  slightest  variation  in  the  re- 
lation of  the  two  motions  should  ever  occur  in  the  course  of 
ages,  is  highly  improbable.  If  such  had  been  the  state  of 
things,  the  correspondence  of  the  two  motions  could  not  have 
been  kept  up  without  her  axial  rotation  varying;  because, 
owing  to  the  secular  acceleration  already  described,  the  moon, 
in  the  couise  of  ages,  varies  her  time  of  revolution,  and  so 
the  two  motions  would  cease  to  correspond.  But  the  effect  of 
the  attraction  of  the  earth  upon  the  slightly  elongated  lunar 
globe  is  such  that  if  the  two  motions  are,  in  the  beginning, 
very  near  together,  not  only  will  the  axial  rotation  accommo- 
date itself  to  tlie  orbital  revolution  around  the  earth,  but  as 
the  latter  varies,  the  former  will  vary  with  it,  and  thus  the 
correspondence  will  be  kept  up. 

Figure^  Rotation^  and  Lihration  of  the  Moon. — Supposing  the 
shape  of  the  moon  to  be  the  same  as  if  it  were  a  fluid  mass, 
or  covered  by  an  ocean,  it  will  be  an  ellipsoid  with  three  un- 
equal axes.  The  shortest  axis  will  be  that  around  which  it 
revolves,  which  is  not  very  far  from  being  perpendicular  to 
the  ecliptic.  The  next  longest  is  that  which  lies  in  the  direc- 
tion in  which  the  moon  moves ;  while  the  longest  of  all  is 
that  which  points  towards  the  earth.  The  reason  that  the 
polar  axis  is  the  shortest  is  the  same  which  makes  the  polar 
axis  of  the  earth  the  shortest,  that  is,  tlie  centrifugal  force 
generated  by  the  revolution  round  that  axis.  If  we  consid- 
ered only  the  action  of  this  force,  we  should  conclude  that  the 
moon,  like  the  earth,  was  an  oblate  spheroid,  the  equator  bs- 


314  THE  SOLAR  SYSTEM. 

iiig  a  perfect  circle.  But  the  attraction  of  the  earth  upon  the 
moon,  tends  to  elongate  it  in  the  direction  of  the  line  joining 
the  two  bodies,  in  the  same  way  that  the  attraction  of  the  moon 
upon  the  earth  generates  a  tide-producing  force  which  we  have 
already  explained.  At  the  centre  of  the  moon  the  attraction 
of  the  earth  and  the  centrifugal  force  of  the  moon  in  its  or- 
bit exactly  balance  each  other.  But  if  w'e  go  to  the  farther* 
/jide  of  the  moon,  the  centrifugal  forie  will  be  greater,  owing 
to  the  lai'ger  orbit  which  that  part  of  the  moon  has  to  de- 
scribe, while  the  attraction  of  the  earth  will  be  less  owing  to 
the  greater  distance  of  the  particles  it  attracts.  Hence,  that 
part  of  the  moon  tends  to  fly  off  from  the  centre  and  from  the 
earth.  On  this  side  of  the  moon  the  case  is  reversed,  the  at- 
tractive force  of  the  earth  exceeding  the  centrifugal  force  of 
those  parts  of  the  moon,  whence  those  parts  are  impelled  by  a 
force  tending  to  draw  them  to  the  earth.  The  effect  would 
be  much  the  same  as  if  a  rope  were  fastened  to  this  side  of 
the  moon,  and  constantly  pulled  towards  the  earth,  while  an- 
other were  fastened  to  the  opposite  side,  and  as  constantly 
pulled  from  the  earth.  Supposing  the  moon  to  be  a  liquid, 
BO  as  to  yield  freely,  it  is  clear  that  the  effect  of  these  forces 
would  be  to  elongate  her  in  the  direction  of  the  earth. 

The  deviations  from  a  spherical  form  produced  by  these 
causes  are  very  minute.  Taking  the  results  of  Lagrange  and 
Newton,  the  mean  axis  would  be  46^  feet  longer  than  the 
shortest  one,  and  the  longest  186  feet  longer  than  the  mean 
one,  or  232^  feet  longer  than  the  shortest  one.*  These  differ- 
ences are  so  much  smaller  thaii  the  average  height  of  the 
lunar  mountains  that  the  irregularities  produced  by  the  latter 
might  entirely  overpower  them ;  but  the  correspondence  be- 
tween the  motions  of  rotation  and  revolution  of  the  moon 
shows  that  there  must  be,  on  the  average,  a  real  elongation  in 


*  These  numbers  are,  peiUaps,  not  strictly  correct.  Tlie  extension  of  18G  feet 
was  deduced  by  Newton  from  a  comparison  of  the  distorting  powers  of  the  centrif- 
ugal force  of  the  earth  with  that  of  the  force  we  have  just  described.  He  seems 
to  have  overlooked  the  fact  that  the  smaU  denbity  of  thtJ  moon  will  cause  the 
elongation  to  be  greater. 


THE  MOON.  315 

the  direction  of  the  earth.  This  correspondence  is  kept  up  by 
the  slight  additional  attraction  of  the  earth  upon  this  extension 
of  the  moon  towards  the  earth,  combined  with  the  additional 
centrifugal  force  of  the  extension  on  the  other  side.  Although 
tliese  forces  are  not  by  any  means  the  same  as  the  distorting 
forces  already  described,  they  may  be  represented  in  the  same 
way  by  two  ropes,  one  of  which  pulls  the  protuberance  on  this 
side  towards  the  earth,  while  the  other  pulls  the  protuberance 
on  the  other  side  from  it.  If  the  two  protuberances  do  not 
point  exactly  towards  the  earth,  the  effect  of  these  two  minute 
forces  will  be  to  draw  them  very  slowly  into  line.  Conse- 
quently, notwithstanding  the  slow  variations  to  which  the  mo- 
tion of  the  moon  around  the  earth  is  subject  in  the  course 
of  ages,  the  attraction  of  the  earth  will  always  keep  this  pro- 
tuberant face  turned  towards  us.  Human  eyes  will  never  be- 
hold the  other  side  of  the  moon,  unless  some  external  force 
acts  upon  her  so  as  to  overcome  the  slight  balancing  force 
just  described,  and  set  her  in  more  or  less  rapid  motion  on 
her  axis.  If  it  is  disappointing  to  reflect  that  we  are  for- 
ever deprived  of  the  view  of  the  other  side  of  our  satellite,  we 
may  console  ourselves  with  the  reflection  that  there  is  not  the 
slightest  reason  to  believe  that  it  differs  in  any  respect  from 
this  side.  The  atmosphere  with  which  it  has  been  covered, 
and  the  inhabitants  with  which  it  has  been  peopled,  are  no 
better  than  the  products  of  a  poetic  imagination. 

The  forces  we  have  just  described  as  tending  to  keep  the 
same  face  of  the  moon  pointed  towards  us  would  not  produce 
this  effect  unless  the  adjustment  of  the  two  motions — that 
around  the  earth,  and  that  on  her  axis — were  almost  perfect 
in  the  beginning.  If  her  axial  rotation  were  accelerated  by  so 
small  an  amount  as  one  revolution  in  two  or  three  years,  there 
is  every  reason  to  believe  that  she  would  keep  on  revolving  at 
the  new  rate,  notwithstanding  the  force  in  question.  The  case 
is  much  like  that  of  a  very  easy-turning  fly-wheel,  which  is 
Slightly  weighted  on  one  side.  If  we  give  the  wheel  a  gentle 
motion  in  one  direction  or  another,  the  weight  will  cause  the 
wheel  to  turn  till  the  heavy  side  is  the  lowest,  and  the  wheel 


316  THE  SOLAR   SYSTEM. 

will  then  vibrate  very  slowly  on  one  side  and  the  other  of  this 
point.  But  if  we  give  the  wheel  a  motion  rapid  enough  to 
carry  its  heavy  side  over  the  highest  point,  then  the  weight 
will  accelerate  the  wheel  while  it  is  falling  as  much  as  it  will 
retard  it  while  rising ;  and  if  there  were  no  friction,  the  wheel 
would  keep  on  turning  indefinitely.  The  question  now  arises, 
How  does  it  happen  that  these  two  motions  are  so  exactly  ad- 
justed to  each  other  that  not  only  is  the  longer  axis  of  the 
moon  pointed  exactly  towards  the  earth,  but  not  the  slightest 
swing  on  one  side  or  the  other  can  be  detected  ?  That  this 
adjustment  should  be  a  mere  matter  of  chance,  without  any 
physical  cause  to  produce  it,  is  almost  infinitely  improbable, 
while  to  suppose  it  to  result  from  the  mere  arbitrary  will  of 
the  Creator  is  contrary  to  all  scientific  philosophy.  But  if  the 
moon  were  once  in  a  partially  fluid  state,  and  rotated  on  her 
axis  in  a  period  different  from  her  present  one,  then  the  enor- 
mous tides  produced  by  the  attraction  of  the  earth,  combined 
with  the  centrifugal  force,  would  be  accompanied  by  a  fric- 
tion which  would  gradually  retard  the  rate  of  rotation,  until 
it  was  reduced  to  the  point  of  exact  coincidence  with  the  rate 
of  revolution  round  the  earth,  as  we  now  find  it.  We  there- 
fore see  in  the  present  state  of  tilings  a  certain  amount  of 
probable  evidence  that  the  moon  was  once  in  a  state  of  par- 
tial fluidity. 

The  force  we  have  just  described  as  drawing  the  protuber- 
ant portion  of  the  moon  towards  the  earth  is  so  excessively 
minute  that  it  takes  it  a  long  time  to  produce  any  sensible  ef- 
fect ;  consequently,  although  the  moon  moves  more  rapidly  in 
some  points  of  her  orbit  than  in  others,  the  force  in  question 
produces  no  corresponding  change  in  the  moon's  rotation. 
The  protuberance  does  not,  therefore,  always  point  exactly  at 
the  earth,  but  sometimes  a  little  one  side,  and  sometimes  a  lit- 
tle the  other,  according  as  the  moon  is  ahead  of  or  behind  her 
mean  place  in  the  orbit.  The  result  is,  that  the  face  which 
the  moon  presents  to  us  is  not  always  exactly  the  same,  there 
being  a  slight  a2)parent  (not  real)  oscillation,  due  to  the  real 
inequality  in  her  orbital  motion.     This  apparent  swaying  is 


THE  MOON.  317 

called  libration,  and  in  consequence  of  it  there  is  nearly  six- 
tenths  of  the  lunar  surface  which  may,  at  one  time  or  another, 
come  into  view  from  the  earth. 

The  Lunar  Day. — In  consequence  of  the  peculiarity  in  the 
moon's  rotation  which  we  have  described,  the  lunar  day  is  29^ 
times  as  long  as  the  terrestrial  day.  Near  the  moon's  equator 
the  sun  shines  without  intermission  nearly  fifteen  of  our  days, 
and  is  absent  for  the  same  length  of  time.  In  consequence, 
the  vicissitudes  of  temperature  to  which  the  surface  is  exposed 
must  be  very  great.  During  the  long  lunar  night  the  temper- 
ature of  a  body  on  the  moon's  surface  would  probably  fall 
below  any  degree  of  cold  that  we  ever  experience  on  the  earth, 
while  during  the  day  it  must  become  hotter  than  anywhere 
on  our  globe. 

Astronomical  phenomena,  to  an  observer  on  the  moon,  would 
exhibit  some  peculiarities.  The  earth  would  be  an  immense 
moon,  going  through  the  same  phases  that  the  moon  does  to 
us ;  but  instead  of  rising  and  setting,  it  would  only  oscillate 
back  and  forth  through  a  few  degrees.  On  the  other  side  of 
the  moon  it  would  never  be  seen  at  alL  The  diurnal  motion 
of  the  stare  would  take  place  in  twenty -seven  of  our  days, 
much  as  they  do  here  every  day,  while,  as  we  have  said,  the 
sun  would  rise  and  set  in  29|-  of  our  days. 

Geography  of  the  Moon.  —  With  the  naked  eye  it  is  quite 
readily  seen  that  the  brilliancy  of  the  moon  is  far  from  uni- 
form, her  disk  being  variegated  with  irregular  dark  patches, 
which  have  been  supposed  to  bear  a  rude  resemblance  to  a 
human  face.  It  is  said  to  have  been  a  fancy  of  some  of  the 
ancient  philosophers  that  the  light  and  dark  portions  were 
caused  by  the  reflection  of  the  seas  and  continents  of  the  ter- 
restrial globe,  though  it  is  hard  to  conceive  of  such  an  opin- 
ion being  seriously  entertained.  The  first  rude  idea  of  the 
real  nature  of  the  lunar  surface  was  gained  by  Galileo  with 
his  telescope.  He  saw  that  the  brighter  portions  of  the  disk 
were  broken  up  witli  inequalities  of  the  nature  of  mountains 
and  craters,  while  the  dark  parts  were,  for  the  most  part, 
smooth  and  uniform.     Here  he  saw  a  strikinor  resemblance  to 


318  TEE  SOLAJR  SYSTEM. 

the  geographical  features  of  our  globe,  and  is  said  to  have  sug. 
gested  that  the  bi'ighter  and  rougher  portions  might  be  conti- 
nents, and  the  dark,  smooth  portions  oceans.  This  view  of  the 
resemblance  to  terrestrial  scenery  is  commemorated  in  Mil- 
ton's description  of  Satan's  shield : 

"  Like  the  moon,  whose  orb 
Through  optic  glass  the  Tuscan  artist  views 
At  evening,  from  the  top  of  Fesole, 
Or  in  Valdarno,  to  descry  new  lands. 
Rivers,  or  mountains  in  her  spotty  globe." 

The  opinion  that  the  dark  portions  of  the  lunar  disk  were 
seas  was  shared  by  Kepler,  Hevelhis,  and  Eicciolus.  The  last 
two  made  maps  of  the  moon  in  which  they  gave  names  to  the 
supposed  seas,  M-hich  names  the  regions  still  bear,  though  they 
are  strikingly  fanciful.  Among  them  are  Ocecmus  Procella- 
rum  (the  Ocean  of  Storms),  Mare  Tranquillitatis  (Sea  of  Tran- 
quillity), Mare  Tnibrium  (Rainy  Sea),  etc.  The  names  of  great 
philosophers  and  astronomers  were  given  to  prominent  feat- 
ures, craters,  etc. 

If  this  resemblance  between  the  earth  and  moon  had  been 
established ;  if  it  had  been  found  that  our  satellite  really  had 
seas  and  atmosphere,  and  was  fitted  for  the  support  of  or- 
ganic life;  still  more,  if  any  evidence  of  the  existence  of  in- 
telliorent  beino^s  had  been  found,  our  interest  in  lunar  geogra- 
phy  would  have  been  immensely  heightened.  But  tlie  more 
the  telescope  was  improved,  the  more  clearly  it  was  seen  that- 
there  was  no  similarity  between  lunar  and  terrestrial  scenery. 
A  very  slight  increase  of  telescopic  power  showed  that  there 
was  no  more  real  smoothness  in  the  regions  of  the  supposed 
seas  than  elsewhere.  The  inequalities  were  smaller  and  hard- 
er to  see  on  account  of  the  darkness  of  color ;  but  that  was 
ail.  The  sun  would  have  been  brilliantly  imaged  back  from 
the  surfaces  of  the  oceans  in  certain  positions  of  the  moon ; 
but  nothing  of  the  kind  was  ever  seen.  The  polariscope 
showed  that  tlie  sun's  rays  did  not  pass  through  any  liquid  at 
the  moon's  surface.  Positive  evidence  of  an  atmosphere  was 
Bought  in  vain.     Supposed  volcanoes  were  traced  to  bright 


THE  MOON  311) 


spots,  illuminated  by  light  from  the  earth.  Inequalities  of 
surface  there  were;  but  in  form  they  were  wholly  different 
from  the  mountains  of  the  earth.     So  the  beautiful  fauciea  of 


7io.  90 — View  of  moon  near  the  third  qimiter.     From  a  photograph  by  Piofeseor  Henn 

Draper. 

the  earlier  astronomers  all  faded  away,  leaving  our  satellite  as 
lifeless  as  an  arid  rock. 

As  the  moon  is  now  seen  and  mapped,  the  difference  be- 
tween the  light  and  dark  portions  is  due  merely  to  a  differ- 
ence in  the  color  of  the  material,  much  of  whicii  seems  to  be 
P  22 


320  THE  SOLAR  SYSTEM. 

darker  than  the  average  of  terrestrial  objects.  The  mountains 
consist,  for  the  most  part,  of  round  saucer-shaped  elevations, 
the  interior  being  flat,  witli  small  conical  mounds  rising  here 
and  there.  Sometimes  there  is  a  single  mound  in  the  centre. 
It  is  very  curious  that  the  figures  of  these  inequalities  in  the 
lunar  surface  can  be  closely  imitated  by  throwing  pebbles 
upon  the  surface  of  some  smooth  plastic  mass,  as  mud  or 
mortar.  They  may  be  well  seen  during  an  eclipse  of  the  sun, 
when  the  contrast  between  the  smoothness  of  the  sun's  limb 
and  the  roughness  of  that  of  the  moon  cannot  escape  notice. 
Their  appearance  is  most  striking  when  the  eclipse  is  annular 
or  total.  In  the  latter  case,  as  the  last  streak  of  sunlight  is 
disappearing,  it  is  broken  up  into  a  number  of  points,  which 
have  been  known  as  "  Baily's  beads,"  from  the  observer  who 
first  described  them,  and  which  are  caused  by  the  sun  shining 
through  the  depressions  between  the  lunar  mountains. 

To  give  the  reader  an  idea  what  the  formation  of  the  lunar 
surface  is,  we  present  a  view  of  the  spot  or  crater  "  Coper- 
nicus," by  Secchi,  taken  from  the  '*  Memoirs  of  the  Royal  As- 
tronomical Society,"  vol.  xxxii.  The  diameter  of  the  central 
portion,  so  much  like  a  fort,  is  about  45  or  50  miles. 

Among  the  most  curious  and  inexplicable  features  of  the 
moon's  surface  are  the  long  narrow  streaks  of  white  material 
which  radiate  from  certain  points,  especially  from  the  great 
crater  Tycho.  Some  of  these  can  be  traced  more  than  a 
thousand  miles.  The  only  way  in  Mhich  their  formation  has 
been  accounted  for  is  by  supposing  that  in  some  former  age 
immense  fissures  were  formed  in  the  lunar  surface  which  were 
subsequently  filled  by  an  eruption  of  this  white  matter  which 
forms  the  streaks. 

Has  the  Mooji  an  Atmosphere?  —  This  question  may  be  an- 
swered by  saying  that  no  evidence  of  a  lunar  atmosphere 
entitled  to  any  weight  has  ever  been  gathered,  and  that  if 
there  is  such  an  atmosphere,  it  is  certainly  not  ^^  part  the 
density  of  the  earth's  atmosphere.  The  most  delicate  known 
test  of  an  atmosphei-e  is  afforded  by  the  behavior  of  a  star 
when  in  apparent  contact  with  the  limb  of  the  moon.     In  this 


THE  MOON. 


821 


Fig.  si.— Lunar  crater  ■'Coperuicuti,"  after  teecchi. 

position  the  rays  of  light  coining  from  the  star  would  pass 
through  the  lunar  atmosphere,  and  be  refracted  by  twice  the 
horizontal  refraction  of  that  atmosphere.  The  star  would 
then  be  apparently  thrown  out  of  its  true  position  in  the  di- 
rection from  the  moon'T  centre  by  the  amount  of  tbis  double 
refraction.  But  obsevvations  of  stars  in  this  position,  at  the 
moment  when  the  lirab  of  the  moon  passes  over  them,  have 
never  indicated  the  slightest  displacement.  It  is  certain  that, 
had  the  displacement  been  decidedly  in  excess  of  half  a  sec- 
ond, it  would  have  been  detected )  tlierefore,  the  double  hori- 
zontal refraction  of  the  lunar  atmosphere,  if  any  exist,  must 
be  as  small  as  half  a  second.*  The  corresponding  refraction 
of  the  earth's  atmosphere  is  4000  seconds.     Therefore,  the  re- 


*  A  simfiar  test  is  afforded  by  the  occultation  of  a  i)lanet,  especially  Saturn  or 
Venus,  the  limb  of  which  would  be  a  little  flattened  as  it  touclied  tlie  moon.  The 
writer  looked  very  carefully  for  this  appearance  during  an  unusually  favorable  oc- 
cultation of  Saturn  which  occurred  on  Aug.  Gth,  1876,  without  seeing  a  trace  of  it. 


322  THE  SOLAR  SYSTEM. 

fractive  power  of  the  lunar  atmosphere  cannot  be  much  in  ex- 
cess of  -g-oVo  that  of  the  earth's,  and  certainly  falls  below  -suVjr- 

Without  an  atmosphere  no  water  or  other  volatile  fluid  can 
exist  on  the  moon,  because  it  would  gradually  evaporate  and 
form  an  atmosphere  of  its  own  vapor.  The  evaporation  would 
not  cease  till  the  pressure  of  the  vapor  became  equal  to  its 
elastic  force  at  the  mean  temperature  of  tlie  moon.  If  this 
temperature  were  as  low  as  the  freezing-point,  the  pressure  of 
an  atmosphere  of  water  vapor  would  be  xru-  that  of  our  at- 
mosphere. So  dense  an  envelope  could  not  fail  of  detection 
with  our  present  means  of  observation. 

The  question  whether  any  change  is  taking  place  on  the 
surface  of  the  moon  is  one  of  interest.  Hitherto,  the  pre- 
ponderance of  evidence  has  been  against  the  idea  of  any 
change.  It  is  true  that  a  few  yeai-s  ago  there  was  a  great 
discussion  in  the  astronomical  world  about  a  supposed  change 
in  the  aspect  of  the  spot  Linna?us,  which  was  found  not  to 
present  the  same  appearance  as  on  Beer  and  Miidler's  map. 
But  careful  scrutiny  showed  that,  owing  to  some  peculiarity 
of  its  surface,  this  spot  varied  its  aspect  according  to  the 
manner  in  which  it  was  illuminated  by  the  sun,  and  these 
variations  appear  to  be  sufficient  to  account  for  the  supposed 
change.  To  whatever  geological  convulsions  the  moon  may 
have  been  subjected  in  ages  past,  it  seems  as  if  she  had  now 
reached  a  state  in  which  no  further  change  was  to  take  place, 
unless  by  the  action  of  some  new  cause.  This  will  not  seem 
sui-prising  if  we  reflect  what  an  important  part  the  atmosphere 
plays  in  the  changes  which  are  going  on  on  the  surface  of  the 
earth.  The  growth  of  forests,  the  formation  of  deltas,  the 
washing-away  of  mountains,  tlie  disintegration  and  blacken- 
ing of  rocks,  and  the  decay  of  buildings,  are  all  due  to  the 
action  of  air  and  water,  the  latter  acting  in  the  form  of  rain. 
Changes  of  temperature  powerfully  re-enforce  the  action  of 
these  causes,  but  are  not  of  themselves  sufficient  to  produce 
any  effect.  Now,  on  the  moon,  there  being  neither  air,  wa- 
ter, rain,  frost,  nor  organic  matter,  the  causes  of  disintegra. 
tion  and  decay  are  all  absent.     A  marble  building  erected 


THE  MOON.  323 

upon  the  surface  of  the  moon  would  remain  century  after 
century  just  as  it  was  left.  It  is  true  that  there  miglit  be 
bodies  so  friable  that  the  expansions  and  contractions  due  to 
the  great  changes  of  temperature  to  which  the  surface  of  the 
moon  is  exposed  would  cause  them  to  crumble.  But  whatev- 
er crumbling  miglit  thus  be  caused  would  soon  be  done  with, 
and  then  no  further  change  would  occur. 

Light  and  Heat  of  the  Moon. — That  the  sun  is  many  times 
brighter  than  the  moon  is  evident  to  the  eye;  but  no  one 
judging  by  the  unaided  eye  would  suppose  the  disparity  to  be 
so  great  as  it  really  is.  It  is  found  by  actual  trial  that  the 
light  of  the  sun  must  be  diminislied  several  hundred  thousand 
times  before  it  becomes  as  faint  as  the  full  moon.  The  results 
of  various  experiments  range  between  300,000  and  800,000. 
Professor  G.  B.  Bond,  of  Cambridge,  found  the  ratio  to  be 
470,000.  The  most  careful  determination  yet  made  is  by 
Zcillner,  who  finds  the  sun  to  give  619,000  times  as  much 
light  as  the  full  moon.  This  result  is  probably  quite  near 
the  truth. 

The  moon  does  not  shine  by  sunlight  alone.  Whenever 
the  narrow  crescent  of  the  new  moon  is  seen  through  a  clear 
atmosphere,  her  whole  surface  may  be  plainly  seen  faintly  il- 
luminated. This  appearance  is  known  as  "  the  old  moon  in 
the  new  moon's  arms."  The  faint  light  thus  shed  upon  the 
dark  parts  of  the  moon  is  reflected  from  the  earth.  An  ob- 
server on  the  moon  would  see  the  earth  in  his  sky  as  a  large 
moon,  much  larger  than  the  moon  is  seen  by  us.  When  it  is 
new  moon  with  us,  it  would  he  full  earth,  if  we  may  be  allowed 
the  term,  to  an  observer  on  this  side  of  the  moon.  Hence, 
under  those  circumstances,  most  of  the  lunar  hemisphere  hid- 
den by  the  sun  is  illuminated  by  earth-light,  or  by  sunlight  re- 
flected by  the  earth,  and  is  thus  rendered  visible.  The  case 
is  the  same  as  if  an  observer  on  the  moon  should  see  the  dark 
hemisphere  of  the  earth  by  the  light  of  the  full  moon. 

As  the  moon  reflects  the  light  ct  the  sun,  so  also  must  she 
reflect  his  heat.  Besides,  she  must  radiate  off  whatever  heat 
she  absorbs  from  the  sup-.    Hence,  we  must  receive  some  heat 


324  THE  SOLAR  SYSTEM. 

from  the  moon,  though  calculation  will  show  tlie  quantity  to 
be  so  small  as  to  defy  detection  with  tlie  most  delicate  ther- 
mometer, the  average  quantity  being  only  -s-g-oVo  o  P^^'t  of  that 
received  from  the  sun.  As  the  direct  rays  of  the  sun  will  not 
raise  the  black-bulb  thermometer  more  than  50  or  60  degrees 
above  the  temperature  of  the  air,  those  of  the  moon  cannot 
raise  it  more  than  -^  o^o  o  of  a  degree.  By  concentrating  the 
rays  in  tlie  focus  of  a  telescope  of  large  aperture  and  compar- 
atively short  focal  length,  the  temperature  might  be  increased 
a  hundred  times  or  more  ;  but  even  then  we  should  only  have 
an  increase  of  J^  of  a  degree.  Even  this  increase  might  be 
unattainable,  for  the  reason  that  tlie  heat  radiated  by  the 
moon  would  not  pass  through  glass.  It  is,  therefore,  only 
since  the  discovery  of  thermo  electricity  and  the  invention  of 
the  thermo-electric  pile  that  the  detection  of  the  heat  from 
the  moon  lias  been  possible.  The  detection  is  facilitated  by 
using  a  reflecting  telescope  to  concentrate  the  lunar  rays, 
because  the  moon  is  not  hot  enough  to  radiate  such  heat  as 
will  penetrate  glass.  Lord  Rosse  and  M.  Marie  -  Davj^,  of 
Paris,  have  thus  succeeded  in  measuring  the  heat  emanating 
from  the  moon.  The  former  sought  not  merely  to  determine 
the  total  amount  of  heat,  but  how  much  it  varied  from  one 
phase  of  the  moon  to  the  other,  and  what  portion  of  it  was 
the  reflected  heat  of  the  sun,  and  what  portion  was  radiated 
by  the  moon  lierself ,  as  if  she  were  a  hot  body.  lie  found 
that  from  new  to  full  moon,  and  thence  round  to  new  moon 
again,  the  quantity  of  heat  received  varied  in  the  same  way 
with  the  quantity  of  light ;  that  is,  there  was  most  at  full- 
moon,  and  scarcely  any  when  the  moon  was  a  thin  crescent. 
That  only  a  small  proportion  of  the  total  heat  emitted  was  the 
reflected  heat  of  the  sun,  was  shown  by  the  fact  that  while  86 
per  cent,  of  solar  heat  passes  througli  glass,  only  12  per  cent, 
of  lunar  heat  does  so.  This  absorption  by  glass  is  well  known 
to  be  a  property  of  the  heat  radiated  bv  ji  body  which  is  not 
itself  at  a  high  temperature.  The  same  result  was  indicated 
in  another  way,  namely,  that  while  the  8un  is  found  by  Zoll* 
ner  to  give  618,000  times  as  much  \\^\i-  as  the  moon,  \\  orCij 


THE  MOON.  325 

gives  82,600  times  as  ninch  heat.  Tluis  botli  the  ratio  of  solar 
to  lunar  heat,  and  the  proportion  of  the  latter  wliich  is  ab- 
sorbed by  glass,  agree  in  indicating  that  about  six-sevenths  of 
the  heat  received  from  the  moon  is  radiated  by  the  latter, 
owing  to  the  temperature  of  her  surface  produced  by  the  ab- 
sorption of  the  sun's  rays. 

Lord  Rosse  was  thus  enabled  to  estimate  the  change  of 
temperature  of  the  moon's  surface  according  as  it  was  tui-ned 
towards  or  from  the  sun,  and  found  it  to  be  more  than  SOO'^ 
Fahrenheit.  But  there  was  no  way  of  determining  the  tem- 
peratures themselves  with  exactness.  Probably  when  the  sun 
does  not  sliine  the  temperature  is  two  or  three  hundred  de- 
grees below  zero,  and  therefore  below  any  ever  known  on  the 
earth;  while  under  the  vertical  sun  it  is  as  much  above  zero, 
and  therefore  hotter  than  boiling  water. 

Effect  of  the  Afoon  on  the  Earth. — We  have  already  explained, 
in  treating  of  gravitation,  how  the  attraction  of  the  moon 
causes  tides  in  the  ocean.  This  is  one  of  the  best-known  ef- 
fects of  lunar  attraction.  It  is  known  from  theory  that  a  sim- 
ilar tide  is  produced  in  the  air,  affecting  the  height  of  the  ba- 
rometer ;  but  it  is  so  minute  as  to  be  entii'ely  masked  by  the 
changes  constantly  going  on  in  the  atmospheric  pressure  from 
other  causes.  There  is  also  reason  to  believe  that  the  occur- 
rence of  earthquakes  may  be  affected  by  the  attraction  of  the 
moon;  but  this  is  a  subject  which  needs  further  investiga- 
tion before  we  can  pronounce  with  certainty  on  a  law  of  con- 
nection. 

Thus  far  there  is  no  evidence  that  the  moon  directly  affects 
the  earth  or  its  inhabitants  in  any  other  way  than  by  her  at- 
traction, which  is  so  minute  as  to  be  entirely  insensible  except 
in  the  ways  we  have  described.  A  striking  illustration  of  the 
fallibility  of  the  human  judgment  when  not  disciplined  by  sci- 
entific tiaining  is  afforded  by  the  opinions  which  have  at  vari- 
ous times  obtained  currency  respecting  a  supposed  influence 
of  the  moon  on  the  weather.  Neither  in  the  reason  of  the 
case  nor  in  observations  do  we  find  any  real  support  for  such 
a  theory.    It  must,  however,  be  admitted  that  opinions  of  this 


326  THE  SOLAR  SYSTEM. 

character  are  not  confined  to  the  uneducated.  In  scientific 
literature  several  papers  are  found  in  which  long  series  of  me- 
teorological observations  are  collated, Mhich  indicate  that  tlie 
mean  temperature  or  the  amount  of  rain  had  been  subject  to 
a  sliglit  variation  depending  on  the  age  of  the  moon.  But 
there  was  no  reason  to  believe  that  these  changes  arose  from 
any  other  cause  than  the  accidental  vicissitudes  to  which  the 
weather  is  at  all  times  subject.  There  is,  perhaps,  higher  au- 
thority for  the  opinion  that  the  ravs  of  the  full  moon  clear 
away  clouds ;  but  if  we  reflect  that  the  effect  of  the  sun  it- 
self in  this  respect  is  not  very  noticeable,  and  tliat  the  full 
moon  gives  only  ^  ^  ^  „  ^^  of  the  heat  of  the  sun,  this  opinion 
will  appear  extremely  improbable. 

§  6.  The  Planet  Mars. 

The  fourth  planet  in  the  order  of  distance  from  the  sun, 
and  the  next  one  outside  the  orbit  of  the  earth,  is  Mars.  Its 
mean  distance  from  the  sun  is  about  141  millions  of  miles. 
The  eccentricity  of  its  orbit  is  such  tiiat  at  perihelion  it  is  only 
128  millions  of  miles  from  the  sun,  while  in  aphelion  it  is  154 
millions  distant.  It  is,  next  to  Mercury,  the  smallest  of  the 
primarv  planets,  its  diameter  being  little  more  than  4000 
miles.  It  makes  one  revolution  in  its  orbit  in  less  than  two 
years  (more  nearly  in  687  days,  or  4:Sh  days  short  of  two  Ju- 
lian years).  If  the  period  were  exactly  two  years,  it  would 
make  one  revolution  while  the  earth  made  two,  and  the  oppo- 
sitions would  occur  at  intervals  of  two  years.  But,  going  a 
little  faster  than  this,  it  takes  the  earth,  on  the  average,  fifty 
days  over  the  two  yeai"s  to  catch  up  to  it.  The  times  of  oppo- 
sition are  shown  in  the  following  table  : 

1884.  ..January  .31st.    I     18S8. .  .April  lOtli.  I     1892.  .  .August  2d. 

1886.  .  .March  6th.        |     1890. .  .Mav  27ili.  I     1894. .  .October  16th. 

The  times  of  several  subsequent  o]->positions  may  be  found 
with  sufiicient  exactness  for  the  identification  of  the  planet  by 
adding  two  yeai-s  and  two  months  for  every  opposition,  except 
during  the  spring   months,  when  onlv  one  month  is  to  be 


THE  PLANET  MARS.  327 

added.  Oppositions  Avill  occur  in  December,  1896,  and  Feb- 
ruary, 1899.  At  the  times  of  opposition  Mars  rises  wnen  the 
snn  sets,  and  may  be  seen  during  the  entire  niglit. 

Aspect  of  Mars. — Mars  is  easily  recognized  with  the  naked 
sye  when  near  its  opposition  by  its  fiery-red  h'ght.  It  is  much 
more  brilh'ant  at  some  oppositions  than  at  others,  but  always 
exceeds  an  ordinary  star  of  the  first  magnitude.  The  varia- 
tions of  its  brilliancy  arise  from  the  eccentricity  of  its  orbit, 
and  the  consequent  variations  of  its  distance  from  the  earth 
and  the  snn.  The  perihelion  of  Mars  is  in  the  same  longitude 
m  which  the  earth  is  on  August  27th;  and  Avhen  an  opposition 
occurs  near  that  date,  the  planet  is  only  35  millions  of  miles 
from  the  earth.  This  is  about  the  closest  approach  Avhich  the 
two  planets  can  ever  make.  When  an  opposition  occurs  in 
February  or  March  the  planet  is  near  its  aphelion — 154  mill- 
ions of  miles  fi'om  the  sun  and  G2  millions  from  the  earth. 
The  result  of  these  variations  of  distance  is  that  Mars  is  more 
than  four  times  brighter  when  an  opposition  occurs  in  August 
or  September  than  when  it  occurs  in  February  or  March.  The 
opposition  of  1877  (September  5th)  was  quite  remarkable  in 
this  respect,  as  it  occurred  only  9  days  after  the  planet  passed 
its  perihelion.  The  near  approach  to  the  earth  at  this  time  is 
rendered  memorable  by  the  discovery  of  two  satellites. 

Mars  has  been  an  interesting  object  of  telescopic  research 
from  the  fact  that  it  is  the  planet  wliich  exhibits  the  greatest 
analogy  with  our  earth.  The  equatorial  regions,  even  with  a 
small  telescope,  can  be  distinctly  seen  to  be  divided  into  light 
and  dark  portions,  which  some  observers  suppose  to  be  conti- 
nents and  oceans.  Around  eacli  pole  is  a  region  of  brilliant 
white,  which  the  same  class  of  astronomers  suppose  to  be  due 
to  a  deposit  of  snow.  The  outlines  of  the  dark  and  light  por- 
tions are  sometimes  so  hard  to  trace  as  to  give  rise  to  the  sus- 
picion of  clouds  in  a  Martial  atmospliere.  At  the  same  time, 
a  single  look  at  Mars  through  a  large  telescope  would  convince 
most  observers  that  these  resemblances  to  our  earth  have  a 
very  small  foundation  in  observation,  tlie  evidence  being  neg- 
ative rather  than  positive.     It  must  be  said  in  their  favo?'  *liat 


328 


THE  SOLAR  SYSTEM. 


if  our  earth  were  viewed  at  the  distance  at  which  we  y'wv, 
Mars,  and  with  the  same  optical  power,  it  would  present  a 
similar  telescopic  aspect.     But  it  is  also  possible  that  if  the 

optical  power  of  our  tele- 
scopes were  so  increased 
that  we  could  see  Mars  as 
from  a  distance  of  a  thou- 
sand miles,  the  resemblances 
would  all  vanish  as  com- 
pletely as  they  did  in  the 
case  of  the  moon. 

So  many  drawings  of 
Mars  in  various  positions 
have  been  made  by  the  nu- 
meious  observers  who  have 
studied  it,  that  it  has  be- 

FiG.  82.— The  plauet  Mars  on  June  23d,  1ST5,  at  10 

hours  46  minutes,  as  seen  by  Piofes^soiHoldeu    COme    pOSSlblC    tO    COUStrUCt 

with  the  great  Washington  teiesci^e.  tolerably  accuratc  maps  of 

the  surface  of  the  plauet.  We  give  a  copy  of  one  of  these 
sets  of  maps  by  Kaiser,  the  late  Leyden  astronomer.  Kaiser 
does  not  pretend  to  call  the  different  regions  continents  and 
oceans,  but  merely  designates  them  as  light  and  dark  jiortions. 


Fr«.  S3. — Map  of  Mars,  after  Kaiser,  on  Mercator's  projection. 

Rotation  of  Mars. — Mars  is  the  only  planet  besides  the  earth 
of  which  we  can  be  sure  that  the  time  of  axial  rotation  ad- 
mits of  being  determined  with  entire  precision.  Drawings  by 
Ilooke,  two  centuries  ago,  exhibit  markings  which  can  still  bo 
recognized,  and  from  a  comparison  of  them  with  recent  ones 
Mr.  Proctor  has  fomid  for  the  period  of  rotation  24  hours  37 


THE  PLANET  MAES. 


329 


minutes  22.73  seconds,  which  he  considers  correct  within  three 
or  four  liundredths  of  a  second.  The  equator  of  Mars  is  in- 
clined to  the  plane  of  its  orbit  about  27°,  so  that  the  vicissitudes 
of  the  seasons  are  greater  on  Mars  than  on  the  eartli  in  the  pro- 
portion of  27°  to  23|°.  Owing  to  this  great  obliquity,  we  can 
sometimes  see  one  pole  of  the  planet,  and  sometimes  the  other, 
from  the  earth.     When  in  longitude  350°,  that  is,  in  the  same 


l^iG.  84.— Northern  hemiephere  of  Mars.  Fig.  85.— Soiuhern  hemisphere  of  Mars. 

direction  from  the  sun  in  which  the  earth  is  situated  on  Sep- 
tember 10th,  the  south  pole  of  the  planet  is  inclined  towards 
the  sun;  and  if  the  planet  is  then  in  opposition,  it  will  be  in- 
clined towards  the  earth  also,  so  that  we  can  see  the  region  of 
the  planet  to  a  distance  of  27°  beyond  the  pole.  At  an  op- 
position in  March  the  north  pole  of  the  planet  is  inclined  tow- 
ards the  sun,  and  towards  the  earth  also.  We  have  just  seen 
that  Mars  is  much  farther  at  the  latter  oppositions  tlian  at  the 
former,  so  that  we  can  get  much  better  views  of  the  south  pole 
of  the  planet  than  of  the  north  pole. 

Satellites  of  Mars. — On  the  night  of  August  11th,  1877, 
Professor  Asaph  Hall,  while  scrutinizing  the  neighborhood  of 
Mars  with  the  great  equatorial  of  the  Washington  Observato- 
ry, found  a  small  object  about  80  seconds  east  of  the  planet. 
Cloudy  weather  prevented  further  observation  at  that  time; 
but  on  the  night  of  the  16th  it  was  again  found,  and  two 
hours'  observation  showed  tliat  it  followed  the  planet  in  its 


330  THE  SOLAR  SYSTEM. 

orbital  motion.  Still,  fearing  that  it  might  be  a  small  planet 
which  chanced  to  be  in  the  neighborhood,  Professor  Hall 
waited  for  another  observation  before  announcing  his  discov- 
ery. A  rough  calculation  from  the  observed  elongation  of  the 
satellite  and  the  known  mass  of  Mars  show^ed  that  the  period 
of  revolution  would  probably  be  not  far  fi-om  29  hours,  and 
that,  if  the  object  were  a  satellite,  it  would  be  hidden  during 
most  of  the  following  night,  but  would  reappear  near  its  orig- 
inal position  towards  morning.  This  prediction  was  exactly 
fulfilled,  the  satellite  emerging  from  the  planet  about  four 
o'clock  on  the  morning  of  August  ISth. 

But  this  was  not  all.  The  reappearance  of  the  satellite  was 
followed  by  tlie  appearance  of  another  object,  much  closer  to 
the  planet,  which  proved  to  be  a  second  and  inner  satellite. 
The  reality  of  both  objects  was  abundantly  confirmed  by  obser- 
vations on  the  following  nights,  not  only  at  Washington,  but  at 
the  Cambridge  Observatory,  by  Professor  Pickering  and  his  as- 
sistants, and  at  Cambridgeport,  by  Messrs.  Alvan  Clark  &  Sons. 

The  most  extraordinaiy  feature  of  the  two  satellites  is  the 
proximity  of  the  inner  one  to  the  planet,  and  the  rapidity  of 
its  revolution.  The  shortest  period  hitherto  known  is  that  of 
the  inner  satellite  of  Saturn — 22  hours  37  minutes.  But  the 
inner  satellite  of  Mars  goes  round  in  7  hours  38  minutes.  Its 
distance  from  the  centre  of  the  planet  is  about  6000  miles, 
and  from  the  surface  less  than  4000.  If  there  are  any  as- 
tronomers on  Mai's  with  telescopes  and  eyes  like  ours,  they 
can  readily  find  out  whether  this  satellite  is  inhabited,  the  dis- 
tance being  less  than  one-sixtieth  that  of  the  moon  from  us. 

That  kind  of  near  approach  to  simple  relationships  between 
the  times  of  revolution  is  found  here  which  we  see  in  the  sat- 
ellites of  Jupiter  and  Saturn.  The  inner  satellite  of  Mars  re- 
volves in  very  nearly  one-fourth  the  period  of  the  outer  one, 
these  times  being,  „     „. 

Outer  satellite 30     18 

One-fourth  this  period 7    34^ 

Period  of  inner  satellite 7    39 

These  satellites  may  also  be  put  down  as  by  far  the  smallest 


THE  SMALL  PLANETS. 


331 


heavenly  bodies  yet  known.  It  is  hardly  possible  to  make 
anything  like  a  numerical  estimate  of  their  diameters,  because 
they  are  seen  in  the  telescope  only  as  faint  points  of  light ; 
and,  having  no  sensible  surface,  no  such  thing  as  a  measure 
of  the  diameters  is  possible.  The  only  datum  on  which  an 
estimate  can  be  founded  is  the  amount  of  light  which  they 
give.  The  writer  judged  the  magnitude  of  the  outer  one  to 
be  between  the  eleventh  and  twelfth.  According  to  the  esti- 
mate of  Zollner,  Mars  itself,  at  this  opposition,  is  three  magni- 
tudes brighter  tlian  a  first-magnitude  star.  The  difference  of 
brilliancy  between  Mars  and  the  outer  satellite  is,  therefore, 
represented  by  thirteen  or  fourteen  orders  of  magnitude. 
From  this,  it  would  follow  that  Mars  gives  from  200,000  to 
500,000  times  as  much  light  as  the  satellite  ;  and  if  both  are  of 
the  same  liglit-jeflecting  power,  the  diameter  of  the  satellite 
would  be  from  6  to  10  miles.  It  may  be  as  small  as  5  miles, 
or  as  great  as  20,  but  is  not  likely  to  lie  far  without  these 
limits.  The  inner  satellite  is  much  brighter  than  the  outer 
one,  and  its  diameter  probably  lies  between  10  and  40  miles. 


FiQ.  86a.— Apparent  orbits  of  the  satellites  of  Mars  in  ISTT,  as  observed  and  laid  down  by 

Professor  Hall. 

§  7.  The  Small  Planets. 

It  was  impossible  to  study  the  solar  system,  as  it  was  known 
to  modern  astronomy  before  the  beginning  of  the  present  cen- 
tury, without  being  struck  by  the  great  gap  which  existed  be- 
tween Mars  and  Jupiter.  Except  this  gap,  all  the  planets  then 
known  succeeded  each  other  according  to  a  tolerably  regular 


332  THE  SOLAR  SYSTEM. 

law,  and  by  interpolating  a  single  planet  at  nearly  double  the 
distance  of  Mars  the  order  of  distances  would  be  complete. 
The  idea  that  an  unknown  planet  might  really  exist  in  this 
region  was  entertained  from  the  time  of  Kepler.  So  sure 
were  some  astronomei-s  of  this  that,  in  1800,  an  association  of 
twenty-four  observers  was  formed,  having  for  its  object  a  sys- 
tematic search  for  the  planet.  Tlie  zodiac  was  divided  into 
twenty-four  parts,  one  of  which  was  to  be  searched  through 
by  each  observer.  But  by  one  of  those  curious  coincidences 
which  have  so  frequently  occurred  in  the  history  of  science, 
tlie  planet  was  accidentally  discovered  by  an  outside  astrono- 
mer before  the  society  could  get  fairly  to  work.  On  Januaiy 
1st.  ISOl,  Piazzi,  of  Palermo,  found  a  star  in  the  constellation 
Taurus  which  did  not  belong  there,  and  on  observing  it  the 
night  after,  he  found  that  it  had  changed  its  position  among 
the  surrounding  stars,  and  must,  therefore,  be  a  planet.  He 
followed  it  for  a  period  of  about  six  weeks,  after  which  it  was 
lost  in  the  rays  of  the  sun  without  any  one  else  seeing  it. 
When  it  was  time  to  emerge  again  in  the  following  autumn, 
its  rediscovery  became  a  difficult  problem.  But  the  skill  of  the 
great  mathematician  Gauss  came  to  the  rescue  with  a  method 
by  which  the  orbit  of  any  planetary  body  could  be  complete- 
ly and  easily  determined  from  three  or  four  observations.  He 
was  thus  able  to  tell  observers  where  their  telescopes  must  be 
pointed  to  rediscover  the  planet,  and  it  was  found  without  dif- 
ficulty before  the  end  of  the  year.  Piazzi  gave  it  the  name 
Ceres.  The  orbit  found  by  Gauss  showed  it  to  revolve  between 
Mars  and  Jupiter  at  a  little  less  than  double  the  distance  of 
the  former,  and  therefore  to  be  the  long -thought -of  planet. 
But  the  discovery  had  a  sequel  which  no  one  anticipated,  and 
of  which  we  have  not  yet  seen  the  end.  In  March,  1802,  Gi- 
bers discovered  a  second  planet,  which  was  also  found  to  be 
revolving  between  Mars  and  Jupiter,  and  to  which  he  gave 
the  name  PaUas.  The  most  extraordinary  feature  of  its  orbit 
was  its  great  inclination,  which  exceeded  Z^^.  Gibers  there- 
upon suggested  his  celebrated  hypothesis  that  the  two  bodies 
might  be  fragments  of  a  single  planet  which  had  been  sha^ 


THE  SMALL  PLAXETS.  333 

tered  by  some  explosion.  If  snch  were  the  case,  the  orbits  of 
all  the  fragments  would  at  first  intersect  each  other  at  the 
point  where  the  explosion  occnrred-  He  therefore  thought  it 
likely  that  other  fragments  would  be  found,  especially  if  a 
search  were  kept  up  near  the  point  of  intersection  of  the  orbits 
of  Ceres  and  Pallas.  Acting  on  this  idea,  Harding,  of  Lilien- 
thal,  found  a  third  planet  in  1S04,  while  Olbers  found  a 
fourth  one  in  1S07.  These  were  called  Juno  and  Vesia.  The 
former  came  quite  near  to  Olbers's  theory  that  the  orbits 
should  all  pass  near  the  same  point,  but  the  latter  did  not. 
Olbeis  continued  a  search  for  additional  planets  of  this  group 
for  a  number  of  years,  but  at  length  gave  it  up,  and  died 
without  tlie  knowledge  of  any  but  these  four. 

In  Dec-ember,  1S45.  thirty-eight  years  after  the  discovery  of 
Yest.'u  Hencke.  of  Driesen,  being  engaged  in  the  preparation 
of  star-charts,  foujid  a  fifth  planet  of  the  group,  and  tlms  re- 
commenced a  series  of  discoveries  which  have  continued  tiD 
tlie  present  time.  Xo  less  than  three  were  discovered  in  1S47, 
and  at  least  one  has  been  found  every  year  since.  To  show 
the  rate  at  which  discovery  has  gy:-ne  on,  we  divide  the  time 
since  1S45  into  periods  of  five  years  each,  and  give  the  num- 
ber  found  during  each  period : 

To  \Si^ 5  were  discoTcred.  i  In  1S66-70 ?7  were  dSseorered. 

In   IS4<»->tO 8     •'  "  I  "  1S7I-75 45     "  " 

•  ISLU-^V-, 24     '•  "  *MS76-W 62     " 

'•    lS.-«-60 25     '^  "  "1^1-85 U     " 

•  lS6l-«5 23    "  *  I  "  1886-90 49 

Total  known  in  1892 325 

It  will  be  seen  that  the  rate  of  discovery  increased  pretty 
steadily  from  1S46  to  ISSO.  and  since  then  has  fallen  off. 
How  far  this  falling  off  is  due  to  there  being  fewer  left  to 
discover,  and  how  far  to  some  discoverers  having  ceased  to 
look  for  new  ones,  we  cannot  yet  say.  During  the  ten  years 
1S6S-77  nearly  half  the  discoveries  were  made  by  Peters,  of 
Clinton,  and  Watson,  of  Ann  Arbor,  both  of  whom  are  now 
dead.  Since  1S78,  Palisa,  of  Vienna,  and  Charlois,  of  Nice, 
have  been  the  leading  discoverers,  and  are  still  adding  to  their 
laurels.    Palisa  has  now  found  more  than  any  other  astronomer. 


334  THE  SOLAR  SYSTEM. 

American  discoveries  of  these  bodies  were  commenced  by 
Mr.  James  Ferguson,  wlio  discovered  Euphrosyne  at  Washing- 
ton on  September  1st,  ISoi.  lie  was  followed  by  Searle,  who 
discovered  Pandora  at  Albany,  and  Tuttle,  who  discovered 
Clytia  at  Cambridge. 

All  the  planets  of  this  group  are  remarkable  for  their  mi- 
auteness.  The  disks  are  all  so  small  as  to  defy  e.vact  meas- 
urement, presenting  the  appearance  of  mere  stars.  A  rough 
estimate  of  their  diameters  can,  however,  be  made  from  the 
amount  of  light  which  they  reflect;  and  although,  in  the  ab- 
sence of  exact  knowledge  of  their  reflecting  power,  the  results 
of  this  method  are  not  very  certain,  tliey  are  the  best  we  can 
obtain.  It  is  thus  found  that  Ceres  and  Yesta  are  the  largest 
of  the  group,  their  diameters  lying  somewhere  between  200 
and  400  miles ;  while,  if  we  omit  some  very  lately  discovered, 
the  smallest  are  Atalanta,  Maja,  and  Sappho,  of  which  the  di- 
ameters may  be  between  20  and  40  miles.  We  may  safely 
say  that  it  would  take  several  thousand  of  the  largest  of  these 
small  planets  to  make  one  as  large  as  the  earth. 

It  has  sometimes  been  said  that  some  of  these  bodies  are  of 
irregular  shape,  and  thus  favor  Olbers's  hypothesis  that  they 
are  fragments  of  an  exploded  planet.  But  this  opinion  has 
no  other  foundation  than  a  suspected  variability  of  their  light, 
which  may  be  an  illusion,  and  which,  if  it  exists,  might  result 
from  one  side  of  the  planet  being  darker  in  color  than  the 
other.  Tlie  latter  supposition  is  not  at  all  improbable,  as  many 
of  the  satellites  are  known  to  be  variable  from  this  or  some 
analogous  cause.  As  the  supposed  irregularities  of  form  have 
never  been  seen,  and  are  not  necessary  to  account  for  the  va- 
riations of  brilliancy,  tliei'e  is  no  suflicient  reason  for  believing 
in  their  existence. 

Olbers's  Hypothesis.  —  The  question  M'hether  these  bodies 
could  ever  have  formed  a  single  one  has  now  become  one  of 
cosmogony  rather  than  of  astronomy.  If  a  planet  were  shat- 
tered, the  orbit  of  each  fragment  would,  at  first,  pass  through 
the  point  at  which  the  explosion  occurred,  however  widely 
they  might  be  separated  througli  the  rest  of  their  course.    Bat 


THE  SMALL  PLANETS.  335 

owing  to  the  secular  changes  produced  by  the  attractions  of 
tlie  other  planets,  this  coincidence  would  not  continue.  Tiie 
orbits  would  slowly  move  away,  and  after  the  lapse  of  a  few 
thousand  years  no  trace  of  a  common  intersection  would  be 
seen.  It  is,  therefore,  curious  that  Olbers  and  his  contempora- 
ries should  have  expected  to  find  such  a  region  of  intersection, 
as  it  implied  that  the  explosion  had  occurred  within  a  few 
thousand  years.  The  fact  that  the  required  conditions  were 
not  fulfilled  was  no  argument  against  the  hypothesis,  because 
the  explosion  might  have  occurred  millions  of  years  ago,  and 
in  the  mean  time  the  perihelion  and  node  of  each  orbit 
would  have  made  many  entire  revolutions ;  so  that  the  orbits 
would  have  been  completely  mixed  up. 

Desirous  of  seeing  whether  the  orbits  passed  nearer  a  com- 
mon point  of  intersection  in  times  past  than  at  present,  Encke 
computed  their  secular  variations.  The  result  seemed  to  be 
adverse  to  Olbers's  hypothesis,  as  it  showed  that  the  orbits 
were  farther  from  having  a  common  point  in  ages  past  than 
at  present.  But  this  result  was  not  conclusive  either,  because 
he  only  determined  the  rates  at  which  the  orbits  are  now 
changing,  whereas,  as  previously  explained,  the  orbits  of  all 
the  planets  really  go  through  periodic  oscillations ;  and  it  is 
only  by  calculating  these  oscillations  that  their  positions  can 
be  determined  for  very  remote  epochs.  They  have  since 
been  determined  for  some  of  the  planets  in  question,  and  the 
result  seems  to  show  that  the  orbits  could  never  have  intersect- 
ed unless  some  of  them  have,  in  the  mean  time,  been  altei'ed 
by  the  attraction  of  the  small  planets  on  eacli  other.  Sucli  an 
action  is  not  impossible;  but  it  is  impossible  to  determine  it, 
owing  to  the  great  number  of  these  bodies,  and  our  ignorance 
of  their  masses.  AVe  can,  however,  say  that  if  the  explosion 
ever  did  occur,  an  immense  interval,  probably  millions  of 
years,  must  have  elapsed  in  the  mean  time.  A  different  ex- 
planation of  the  group  is  given  by  the  nebular  hypothesis,  of 
which  we  shall  hereafter  speak,  so  that  Olbers's  hypothesis  is 
no  longer  considered  by  astronomers. 

The  planets  in  question  are  distinguished  from  the  others, 

23 


336  THE  SOLAR  SYSTEM. 

not  only  by  their  small  size,  but  by  the  great  eccentricitiefl 
and  inclinations  of  their  orbits.  If  we  except  Mercury,  none 
of  the  larger  planets  lias  an  eccentricity  amounting  to  one- 
tenth  the  diameter  of  its  orbit,  nor  is  any  orbit  inclined  more 
than  two  or  three  degrees  to  the  ecliptic.  Bnt  the  inclina- 
tions of  many  of  the  small  planets  exceed  ten  degrees,  and 
the  eccentricities  frequently  amount  to  a  fourth  of  the  radii 
of  their  orbits.  The  result  is  that  the  same  small  planet  is  at 
very  different  distances  from  the  sun  in  various  points  of  its 
orbit.  Add  to  this  the  fact  that  the  mean  distances  of  these 
bodies  from  the  sun  have  a  pretty  wide  range,  and  we  shall 
iind  that  they  extend  through  a  quite  broad  zone.  The  inside 
edge  of  this  zone  seems  pretty  well  marked,  its  distance  being 
about  180  millions  of  miles  from  the  sun,  or  between  30  and 
40  millions  beyond  the  orbit  of  Mars.  On  the  outside,  it  ter- 
minates more  gradually,  but  nowhere  extends  within  50  mill- 
ions of  miles  of  the  orbit  of  Jupiter.  If  any  of  the  small 
planets  ever  ranged  outside  of  certain  limits,  the  attraction  of 
Mars  or  Jupiter  was  so  great  as  to  completely  derange  their 
orbits,  so  that  we  have  a  physical  law  M'hich  sets  a  limit  to  the 
zone ;  but  whether  the  limit  thus  set  would  coincide  with  the 
actual  limit  we  cannot  at  present  say. 

There  are  also  within  the  limits  of  the  group  certain  posi- 
tions, in  wliich,  if  the  orbits  were  placed,  they  would  be  greatly 
changed  by  the  action  of  Jupiter.  These  positions  are  those 
in  which  the  time  of  revolution  would  be  some  simple  exact 
fraction  of  that  of  Jupiter,  as  ^,  |-,  f ,  y,  etc.  Professor  Daniel 
Kirkwood  has  pointed  out  tlie  curious  fact  that  there  are  gaps 
in  the  series  of  small  planets  corresponding  to  these  periodic 
times.  Whether  these  gaps  are  really  due  to  the  relations  of 
the  periodic  times,  or  are  simply  the  result  of  chance,  cannot 
yet  be  settled.  The  fact  that  quite  a  number  of  the  small 
planets  have  a  period  very  nearly  three-eighths  that  of  Jupiter, 
may  lead  us  to  wait  for  further  evidence  before  concluding 
tliat  we  have  to  deal  witn  a  real  law  of  nature  in  the  cases 
pointed  out  by  Professor  Kirkwood. 

Number  and  Total  Mass  of  the  Small  Planets. — At  present  it 


THE  SMALL  PLANETS.  337 

{8  not  possible  to  set  any  certain  limits  to  the  probable  number 
of  the  small  planets.  Although  a  hundred  and  seventy -two 
are  now  known,  there  is  as  yet  no  sensible  diminution  in  the 
rate  at  w^iich  they  are  being  discovered.  The  question  of 
their  total  number  depends  very  largely  on  whether  there  is 
any  limit  to  their  minuteness.  If  there  is  no  such  limit,  then 
there  may  be  an  indefinite  number  of  them,  too  small  to  be 
found  with  the  telescopes  now  engaged  in  searching  for  them ; 
and  the  larger  tlie  telescopes  engaged  in  the  search,  the  more 
will  be  found.  On  the  other  hand,  if  they  stop  at  a  certain 
limit — say  twenty  miles  in  diameter — we  may  say  with  con- 
siderable confidence  that  their  total  number  is  also  limited, 
and  that  by  far  the  largest  part  of  them  will  be  discovered 
by  the  present  generation  of  astronomers. 

So  far  as  we  can  now  see,  the  preponderance  of  evidence  is 
on  the  side  of  the  number  and  magnitude  being  limited.  The 
indications  in  this  direction  are  that  the  newly  discovered  ones 
are  not  generally  the  smallest  objects  which  could  be  seen 
with  the  telescopes  which  have  made  the  discovery,  and  do 
not  seem,  on  the  average,  to  be  materially  smaller  than  those 
which  were  discovered  ten  years  ago.  It  is  not  likely  that  the 
number  of  this  average  magnitude  which  still  remain  undis- 
covered can  be  very  great,  and  new  ones  will  probably  be 
found  to  grow  decidedly  rare  before  another  hundred  are  dis- 
covered. Then  it  will  be  necessary  to  employ  greater  optical 
power  in  the  search.  If  this  results  in  finding  a  number  of 
new  ones  too  small  to  be  found  with  the  former  telescopes,  we 
shall  have  to  regard  the  group  as  unlimited  in  number.  But 
if  no  such  new  ones  are  thus  found,  it  will  show  that  the  end 
has  been  nearly  reached. 

In  gravitational  astronomy,  the  question  of  the  total  mass 
•of  the  small  planets  is  more  important  than  that  of  their  total 
number,  because  on  this  mass  depends  their  effect  in  altering 
the  motions  of  the  large  planets.  Any  individual  small  planet 
is  so  minute  that  its  attraction  on  the  other  planets  is  entirely 
insensible.  But  it  is  not  impossible  that  the  whole  group 
might,  by  their  combined  action,  produce  a  secular  variation 


338  THE  SOLAR  SYSTEM. 

in  the  form  of  the  orbits  of  Mars  and  Jupiter  which,  in  tho 
course  of  yeai*s,  will  be  clearly  shown  by  the  observations. 
But,  although  accurate  observations  of  these  planets  have  been 
made  for  more  than  a  century,  no  such  effect  has  yet  been  no- 
ticed. Tlie  sura  total  of  their  masses  must,  therefore,  be  much 
less  than  that  of  an  average  planet,  though  we  cannot  say  pre- 
cisely what  the  limit  is.  The  apparent  magnitude  of  those 
which  have  been  discovered  is  entirely  accordant  with  the 
opinion  that  the  mass  of  the  entire  group  is  so  small  that  it 
camiot  make  itself  felt  by  its  attraction  on  the  other  planets 
for  many  years  to  come.  In  fact,  if  their  diameters  be  esti- 
mated from  tlieir  brightness,  in  the  manner  already  indicated, 
we  shall  find  that  if  all  that  are  yet  known  were  made  into  a 
single  planet  the  diameter  would  be  less  than  400  miles ;  and 
if  a  thousand  more,  of  the  average  size  of  tliose  discovered 
since  1850  should  exist,  their  addition  to  the  consolidated 
planet  would  not  increase  its  diameter  to  500  miles.  Such  a 
planet  would  be  only  40V0  ^f  the  bulk  of  the  earth,  and,  un- 
less we  supposed  it  to  possess  an  extraordinary  specific  gravity, 
could  not  much  exceed  ^riroTr  of  the  mass  of  the  earth,  or  -jV  of 
the  mass  of  Mercury.  We  may  fairly  conclude  that  unless 
the  group  of  small  planets  actually  consists  of  tens  of  thou- 
sands of  minute  bodies,  of  which  only  a  few  of  the  brightest 
liave  yet  been  discovered,  their  total  volume  and  mass  are  far 
less  than  those  of  any  one  of  the  major  planets. 

The  number  of  these  bodies  now  known  is  so  great  that  the 
mere  labor  of  keeping  the  run  of  their  motions,  so  that  they 
shall  not  be  lost,  is  out  of  proportion  to  the  value  of  its  results, 
It  is  mainly  through  the  assiduity  of  German  students  that 
most  of  them  are  kept  from  being  lost.  Should  many  more 
be  found,  it  may  be  necessary  to  adopt  the  suggestion  of  an 
aininent  German  astronomer,  and  let  such  of  them  as  seem 
unimportant  go  again,  and  pui-sue  their  orbit  undisturbed  bj? 
telescope  or  computer. 


THE  PLANET  JUPITEB.  339 


CHAPTER  IV. 

THE  OUTER  GROUP  OF  PLANETS. 

§  1.  The  Planet  Jupiter. 

Jupiter  is  the  "giant  planet  "  of  our  system,  his  mass  large- 
ly exceeding  that  of  all  the  other  planets  combined.  His 
mean  diameter  is  about  85,000  miles;  but  owing  to  his  rapid 
rotation  on  his  axis,  his  equatorial  exceeds  his  polar  diameter 


Fi«.  8<5.— Jupiter  ns  seen  with  the  great  Washfngton  telescope,  March  21st,  1876, 15  honr* 
38  miuutes  mean  time.    Drawu  by  Professor  Uoldeo. 

by  5000  miles.  In  volume  he  exceeds  our  earth  about  1300 
itimes,  while  in  mass  he  exceeds  it  about  213  times.  His  spe- 
cific gravity  is,  therefore,  far  less  than  that  of  the  earth,  and 
even  less  than  that  of  water.  His  mean  distance  from  the 
sun  is  480  millions  of  miles,  but,  owing  to  the  eccentricity  of 
his  orbit,  his  actual  distance  ranges  between  457  and  503  mill- 
ions. His  time  of  revolution  is  fifty  days  less  than  twelve 
years. 


840  THE  SOLAB  SYSTEM. 

Jupiter  is  easily  recognized  by  his  brilliant  white  light,  with 
which  he  outshines  every  other  planet  except  Yenus.  To  fa- 
cilitate his  recognition,  we  give  the  dates  of  opposition  during 
a  few  3'ears. 

1888 May  21st.       I     1890 July  30th. 

1889 June  24th. 3    I    1891 September  7th. 

During  the  four  years  following  1891  he  will  be  in  opposi- 
tion, on  the  average  about  five  weeks  later  each  year,  namely, 
about  the  middle  of  October,  1892,  toward  the  end  of  No- 
vember, 1893,  and  so  on.  A  month  or  two  before  opposition 
he  can  be  seen  rising  late  in  the  evening,  while  during  the 
three  months  following  opposition  he  will  always  be  seen  in 
the  early  evening  somewhere  between  south-east  and  south- 
west. 

The  Surface  of  Jupiter. — Except  the  sun  and  moon,  there 
is  no  object  of  our  system  which  has  during  the  last  few  years 
been  the  subject  of  more  careful  examination  than  this  planet. 
The  markings  on  his  surface  are  subject  to  changes  so  great 
and  rapid  that  a  map  of  Jupiter  is  impossible.  But  this  sur- 
face always  presents  a  very  diversified  appearance.  The  ear- 
lier telescopic  observers  described  light  and  dark  belts  as  ex- 
tending across  it.  Until  a  quite  recent  period  it  has  been 
customary  to  describe  these  belts  as  two  in  number,  one  north 
of  the  equator  and  the  other  south  of  it.  Commonly  they  are 
seen  as  dark  bands  on  the  bright  disk  of  the  planet ;  but  it  is 
curious  that  Huyghens  represents  them  as  brighter  than  the 
rest  of  the  surface.  As  telescopic  power  was  increased,  it  was 
seen  that  the  so  -  called  bands  were  of  a  far  more  complex 
structure  than  had  been  supposed,  and  consisted  of  great 
numbers  of  stratified,  cloud-like  appearances  of  the  most  va- 
riegated forms.  These  forms  change  so  rapidly  that  the  face 
of  the  planet  may  change  in  appearance  on  two  successive 
nights.  Tliey  are  most  strongly  marked  at  some  distance 
on  each  side  of  tlie  Jovian  equator,  and  thus  give  rise  to  the 
appearance  of  two  belts  when  a  very  small  or  imperfect  tele- 
scope is  used. 


THE  PLANET  JUPITER.  341 

Both  the  outlines  of  these  belts  and  the  color  of  some  partE 
of  the  planet,  seem  subject  to  considerable  changes.  The 
equatorial  regions,  and  indeed  the  spaces  between  the  belts 
generally,  are  often  of  a  rosy  tinge.  This  coloring  is  some- 
times so  strongl}^  marked  as  to  be  evident  to  the  most  super- 
licial  observer,  .vhile  at  other  times  hardly  a  trace  of  it  can  be 
seen. 

Spots  which  are  much  more  permanent  than  the  ordinar;^ 
marking's  on  the  belt  are  sometimes  visible.  Bv  watchirig 
these  spots  from  day  to  day,  and  measuring  their  position 
upon  the  apparent  disk,  the  time  of  rotation  of  Jupiter  on  his 
axis  has  been  determined.  Commonly  the  spots  are  dark; 
but  on  some  rather  rare  occasions  the  planet  is  seen  with  a 
number  of  small,  round,  bright  spots  like  satellites.  Of  theso 
bright  spots  no  explanation  has  been  given. 


Tio.  87. — View  of  Jupiter,  as  seen  in  Lord  Rosse's  great  telescope  on  February  27th, 
1S61,  at  12  hours  30  minutes. 

From  the  changeability  of  the  belts,  and  indeed  of  nearly  all 
the  visible  features  on  the  surface  of  Jupiter,  it  is  clear  that 
what  we  see  on  that  planet  is  not  the  surface  of  a  solid  nu- 
cleus, but  vaporous  or  cloud-like  formations  which  cover  the 
entire  surface  and  extend  to  a  great  depth  below.  To  all  ap- 
pearance, the  planet  is  covered  with  a  deep  and  dense  atmos- 


342  THE  SOLAR   SYSTEM. 

pliere,  throiigli  which  light  cannot  penetrate  on  account  of 
thick  masses  of  clouds  and  vapor.  In  the  arrangements  oi 
these  clouds  in  streaks  parallel  to  the  equator,  and  in  the 
change  of  their  forms  with  the  latitude,  there  may  be  some- 
thinor  analogous  to  the  zones  of  clouds  and  rain  on  the  earth. 
But  of  late  years  it  has  been  noticed  tliat  the  physical  consti 
tution  of  Jupiter  seems  to  offer  more  analogies  to  that  of  the 
sun  than  to  that  of  the  earth.  Like  the  sun,  he  is  brighter  in 
the  centre  than  near  the  edges.  This  is  shown  in  the  most 
striking  manner  in  the  transits  of  his  satellites  over  his  disk. 
Wlien  the  satellite  first  enters  on  the  disk,  it  commonly  seems 
like  a  bright  spot  on  a  dark  background  ;  but  as  it  approaches 
the  centre,  it  appears  like  a  dark  spot  on  the  bright  back- 
ground of  the  planet.  The  brightness  of  the  centre  is  prob- 
ably two  or  three  times  greater  than  tliat  of  the  limb.  This 
diminution  of  light  towards  the  edge  may  arise,  as  in  the  case 
of  the  sun,  from  the  light  near  the  edge  passing  through  a 
greater  depth  of  atmosphere,  and  thus  becoming  fainter  by 
absorption. 

A  still  more  remarkable  resemblance  to  the  sun  has  some- 
times been  suspected — nothing  less,  in  fact,  than  that  Jupiter 
shines  partly  by  his  own  light.  It  was  at  one  time  supposed 
that  he  actually  emitted  more  light  than  fell  upon  him  from 
the  sun ;  and  if  this  were  proved,  it  would  show  conclusive- 
ly that  he  was  self-luminous.  If  all  the  light  which  the  sun 
shed  upon  tlie  planet  were  equally  reflected  in  every  direction, 
we  might  speak  with  some  certainty  on  this  question ;  but  in 
the  actual  state  of  our  knowledge  we  cannot.  Zollner  has 
found  that  the  brightness  of  Jupiter  may  be  accounted  for  by 
supposing  him  to  reflect  62  per  cent,  of  the  sunlight  which  he 
receives.  But  if  this  is  his  average  reflecting  power,  the  re* 
fleeting  power  of  his  brighter  portions  must  be  much  greater; 
in  fact,  they  are  so  bright  that  they  must  shine  partly  by  their 
own  light,  unless  they  reflect  a  disproportionate  share  of  the 
sunlight  back  in  the  direction  of  the  earth  and  sun.  Clouds 
would  not  be  likely  to  do  this.  On  the  other  hand,  if  we  as- 
sume that  the  planet  emits  any  great  amount  of  light,  we  are 


THE  PLANET  JUPITER.  343 

met  by  the  fact  that,  if  this  were  the  case,  the  satellites  would 
shine  by  this  light  when  they  were  in  the  shadow  of  the 
planet.  As  these  bodies  totally  disappear  in  this  position,  the 
quantity  of  light  emitted  by  Jupiter  must  be  quite  small.  On 
the  whole,  there  is  a  small  probability  that  the  brighter  spots 
of  this  planet  are  from  time  to  time  slightly  self-lumiuons. 

Again,  the  interior  of  Jupiter  seems  to  be  the  seat  of  an 
activity  so  enormous  that  we  can  attribute  it  only  to  a  very 
high  temperature,  like  that  of  the  sun.  This  is  shown  by  the 
rapid  movements  always  going  on  in  his  visible  surface,  which 
frequently  changes  its  aspect  in  a  few  hours.  Such  a  power- 
ful effect  could  hardly  be  produced  by  the  rays  of  the  sun, 
because,  owing  to  the  great  distance  of  the  planet,  he  receives 
only  between  one-twenty-fifth  and  one-thirtieth  of  the  light 
and  heat  which  we  do.  It  is  therefore  probable  that  Jupiter 
is  not  yet  covered  by  a  solid  crust,  as  our  earth  is,  but  that 
his  white-hot  interior,  whether  liquid  or  gaseous,  has  nothing 
to  cover  it  but  the  dense  vapors  to  which  that  heat  gives  rise. 
In  this  case  the  vapors  may  be  self-luminous  when  they  have 
freshly  arisen  from  the  interior,  and  may  rapidly  cool  off  after 
reaching  the  upper  limit  to  which  they  ascend. 

Rotation  of  Jwpiteir. — Owing  to  the  physical  condition  of  Ju- 
piter, no  precisely  determinate  time  of  rotation  can  be  assign- 
ed him,  as  in  the  case  of  Mars,  Without  a  solid  crust  which 
we  can  see  from  time  to  time,  the  observed  times  of  rota- 
tion will  be  those  of  liquid  or  vaporous  formations,  which  may 
have  a  proper  motion  of  their  own.  A  spot  has,  however,  on 
some  occasions  been  observed  for  several  years,  and  it  has 
thus  been  pretty  certainly  determmed  that  the  time  of  rota- 
tion is  about  9  hours  55^  minutes.  The  first  observation  of  & 
spot  of  this  kind  was  made  by  Cassini,  who  found  the  time  of 
rotation  to  be  9  hours  55  minutes  58  seconds.  No  further 
exact  observations  were  made  until  the  time  of  Schroter,  who 
observed  a  number  of  transient  spots  during  1785  and  1786. 
The  times  of  rotation  varied  from  9  hours  55  minutes  to  9 
hours  56  minutes,  from  \vhich  he  concluded  that  heavy  storms 
ragod  on  the  surface  of  the  planet,  and  gave  the  cloudy  masses 
0 


344  THE   SOLAR  SYSTEM. 

which  formed  the  spots  a  motion  of  their  own.  In  November, 
1834,  a  remarkable  spot  was  observed  by  Madler,  of  Dorpat, 
which  Listed  until  the  following  April,  from  which  the  time 
of  rotation  came  out  9  liours  55  minutes  30  seconds. 

The  most  persistent  of  these  phenomena  yet  observed  is  the 
noted  "red  spot,"  whicli  has  been  followed  since  1879,  and  is 
still  visible,  though  very  faint.  For  several  years  it  was  very 
conspicuous.  Whether  it  is  destined  to  fade  away  entirel}', 
or  to  continue  as  a  permanent  feature  of  the  planet's  surface, 
cannot  yet  be  determined.  This  spot  is  found  to  rotate  in  9 
hours  55  minutes  40  seconds,  but  the  period  changes  slightly 
from  time  to  time. 

Kecent  observations  and  researches  indicate  that  the  equa- 
torial regions  of  Jupiter  rotate  in  less  time,  and  with  more  ir- 
regularity, than  the  others,  thus  showing  still  another  analogy 
between  that  planet  and  the  sun. 

§  2.  The  Satellites  of  Jupiter. 

One  of  the  earliest  telescopic  discoveries  by  Galileo  was 
that  Jupiter  was  accompanied  by  four  satellites,  which  re- 
volved round  him  as  a  centre,  thus  forming  a  miniature  copy 
of  the  solar  system.  As  in  the  case  of  spots  on  the  sun,  Gal- 
ileo's announcement  of  this  discovery  was  received  with  in- 
credulity by  those  philosophers  of  the  day  who  believed  that 
everything  in  nature  was  described  in  the  writings  of  Aris- 
totle. One  eminent  astronomer — Clavius  —  said  that  to  see 
the  satellites  one  must  have  a  telescope  which  would  produce 
them;  but  he  changed  his  mind  as  soon  as  he  saw  them  him- 
self. Another  philosopher,  more  prudent,  refused  to  put  his 
eye  to  the  telescope  lest  he  should  see  them  and  be  con- 
vinced. He  died  shortly  afterwards.  "  I  hope,"  said  the  caus- 
tic Galileo,  "  that  he  saw  them  while  on  his  way  to  heaven." 

A  very  small  telescope,  or  even  a  good  opera-glass,  is  suf- 
ficient to  show  these  bodies.  Indeed,  very  strong  evidence  is 
on  record  that  they  have  been  seen  with  the  naked  eye.  That 
they  could  be  seen  by  any  good  eye,  if  the  planet  were  out  of 
the  way,  there  is  no  doubt,  the  difficulty  in  seeing  them  aria^ 


THE  SATELLITES  OF  JUPITER.  345 

ing  from  the  glare  of  the  planet  on  the  eye.  If  the  lenses  of 
the  eye  are  so  transparent  and  pure  that  there  is  no  such 
glare,  it  is  quite  possible  that  the  two  outer  satellites  might 
be  seen,  especially  if  they  should  happen  to  be  close  to- 
gether. 

According  to  the  best  determinations,  which  are,  however, 
by  no  means  certain,  the  diameters  of  the  satellites  of  Jupiter 
range  between  2200  and  3700  miles,  the  third  from  the  planet 
being  the  largest,  and  the  second  the  smallest.  The  volume  of 
the  smallest  is,  therefore,  very  near  that  of  our  moon. 

The  light  of  these  satellites  vaiies  to  an  extent  which  it 
is  difficult  to  account  foi",  except  by  supposing  very  violent 
changes  constantly  going  on  on  their  surfaces.  It  has  some- 
times been  supposed  that  some  of  them,  like  our  moon,  always 
present  the  samij  face  to  Jupiter,  and  that  the  changes  in  their 
brilliancy  are  due  to  differences  in  the  color  of  the  parts  of 
the  satellites  which  are  successively  turned  towards  us  during 
one  revolution  round  the  planet.  But  the  careful  measures 
of  their  light  made  by  Auwers,  of  Berlin,  and  Engelmann,  of 
Leipsic,  show  that  this  hypothesis  does  not  account  for  the 
changes  of  brilliancy,  which  are  sometimes  sudden  in  a  sur- 
prising degree.  The  satellites  are  so  distant  as  to  elude  tele- 
scopic examination  of  their  surfaces.  AVe  cannot,  therefore, 
hope  to  give  any  certain  explanation  of  these  changes. 

The  satellites  of  Jupiter  offer  problems  of  great  difficulty 
to  the  mathematician  who  attempts  to  calculate  the  effect  of 
their  mutual  attractions.  The  secular  vaiiations  of  tlieir  or- 
bits are  so  rapid  that  the  methods  applied  in  the  case  of  the 
planets  cannot  be  applied  here  without  material  alterations. 
The  most  curious  and  interesting  effect  of  their  mutual  at- 
traction is  that  there  is  a  connection  between  the  motions  of 
the  three  inner  satellites  such  as  exists  nowhere  else  in  the 
solar  system.     The  connection  is  shown  by  these  two  laws : 

1.  That  the  mean  motion  of  the  first  satellite  added  to  twice  the 
mean  motion  of  the  third  is  exactly  equcd  to  three  times  the  mean 
motion  of  the  second. 

2.  That  if  to  the  mean  longitude  of  the  first  satellite  loe  add 


346  THE  SOLAR  SYSTEM. 

twice  the  mean  longitude  of  the  third,  and  svhtract  three  times  the 
mean  longitude  of  the  second,  tJie  difference  is  always  180°. 

The  first  of  these  relations  is  shown  in  the  following  table 
of  the  mean  daily  motions  of  the  satellites : 

Satellite     I.  in  one  day  moves 203''.4890 

"        II.        "  "  101°.3748 

"      III.        "  "  50°.3177 

"      IV.         "  "  21°.571l 

Motion  of  Satellite  1 203^4890 

Twice  that  of  Satellite  III 100°.6354: 

Sum 304°.1244 

Three  times  motion  of  Satellite  II 304°.  12U 


It  was  first  found  from  observations  that  the  three  satellites 
moved  together  so  nearly  according  to  this  law  that  no  certain 
deviation  could  be  detected.  But  it  was  not  known  whether 
this  was  a  mere  chance  coincidence,  or  an  actual  law  of  nat- 
ure, till  Laplace  showed  that,  if  they  moved  so  nearly  in  this 
way  as  observations  had  shown  them  to,  there  would  be  an  ex- 
tremely minute  force  arising  fi-om  their  mutual  gravitation, 
sufiicient  to  keep  them  in  this  relative  position  forever.  There 
is,  in  this  case,  some  analogy  to  the  rotation  of  the  moon, 
which,  being  once  started  presenting  the  same  face  to  the 
earth,  is  always  held  in  that  position  by  a  minute  residual  of 
the  earth's  attraction. 

We  have  already  spoken  of  the  discovery  of  the  progressive 
motion  of  light  from  the  eclipses  of  these  satellites,  and  of 
the  uses  of  these  eclipses  for  the  rough  determination  of 
longitudes.  Both  the  eclipses,  and  the  transits  of  their  bodies 
over  the  face  of  Jupiter  afford  interesting  subjects  of  obser- 
vation with  a  telescope  of  sufiicient  power,  say  four  inches  ap- 
erture or  upwards.  To  facilitate  such  observations  the  times 
of  these  phenomena  are  predicted  in  both  the  American  and 
British  Kautical  Almanacs. 

§  3.  /Saturn  and  its  System,  Physical  Aspect,  Belts,  Rotation. 

Satum  is  the  sixth  of  the  major  planets  in  the  order  of  dis- 
tance from  the  sun,  around  which  it  revolves  in  29|^  years  at 


SATURN  AND  HIS  SYSTEM. 


347 


a  mean  distance  of  about  880  millions  of  miles.  In  mass  and 
size  it  stands  next  to  Jupiter,  To  show  the  disparity  in  the 
masses  of  the  planets  we  may  refer  to  the  table  already  given, 
showing  that  although  Saturn  is  not  one -third  the  mass  of 
Jupiter,  it  has  about  three  times  the  mass  of  the  six  planets, 
which  are  smaller  than  itself  put  together.  Its  surroundings 
are  such  as  to  make  it  the  most  magnilicent  object  in  the  solar 
system.     While  no  other  planet  is  known  to  have  more  than 


Fig.  S8.— View  of  Saturn  and  his  rings. 

four  satellites,  Saturn  has  no  less  than  eight.  It  is  also  snr- 
rounded  by  a  pair  of  rings,  the  interior  diameter  of  which  is 
'About  100,000  miles.  The  aspect  of  these  rings  is  subject  to 
great  variations,  for  reasons  which  wnll  soon  appear.  The 
great  distance  of  the  planet  renders  the  study  of  its  details 
difficult  unless  the  highest  telescopic  power  is  applied.  The 
whole  combination  of  Saturn,  his  rings,  and  his  satellites  is 
often  called  the  Saturnian  System. 

The  planet  Saturn  generally  shines  with  the  brilliancy  of  a 


348  THE  SOLAR  SYSTEM. 

moderate  first-magnitude  star,  and  witli  a  dingy,  reddisli  light, 
as  if  seen  through  a  smoky  atmosphere.  Its  apparent  bright- 
ness is,  liowever,  different  at  different  times :  during  the  years 
1876-1879  it  is  fainter  than  the  average,  owing  to  its  ring  be- 
ing: seen  nearly  edo^ewise.  From  1878  till  1885  it  will  con- 
stantly  grow  brighter,  on  account  both  of  the  opening  out  of 
the  ring  and  the  approach  of  the  planet  to  its  perihelion. 
Tlie  times  of  opposition  are  as  follow  : 

1888 January  23(i.    I     1890 February  19th.  |    1892 March  17th, 

1889 February  5th.  I    1891 March  4th.         I    1893 March  30th. 

In  subsequent  years  opposition  will  occur  about  thirteen  days 
later  every  year,  so  that  by  adding  this  amount  to  the  date  for 
each  year  the  oppositions  can  be  found  until  the  end  of  the 
century  without  an  error  of  more  than  a  few  days. 

The  physical  constitution  of  Saturn  seems  to  bear  a  great 
resemblance  to  that  of  Jupiter ;  but,  being  twice  as  far  away, 
it  cannot  be  so  well  studied.  The  farther  an  object  is  from 
the  sun,  the  less  brightly  it  is  illuminated ;  and  the  farther 
from  the  earth,  the  smaller  it  looks,  so  that  there  is  a  double 
difficulty  in  getting  the  finest  views  of  the  more  distant  plan- 
ets. When  examined  under  favorable  circumstances,  the  sur- 
face of  Saturn  is  seen  to  be  diversified  with  very  faint  mark- 
ings; and  if  high  telescopic  powers  are  used,  two  or  more 
^-ery  faint  streaks  or  belts  may  be  seen  parallel  to  its  equator, 
the  strongest  ones  lying  on,  or  very  near,  the  equator.  As  in 
the  case  of  Jupiter,  these  belts  change  theii'  aspect  from  time 
to  time,  but  they  are  so  faint  that  the  changes  cannot  be 
easily  followed.  It  is  therefore,  in  general,  difficult  to  say 
with  certainty  whether  we  do  or  do  not  see  the  same  face  of 
Saturn  on  different  nights ;  and,  consequently,  it  is  only  on 
extraordinary  occasions  that  the  time  of  rotation  can  be  de- 
termined. 

The  first  occasion  on  which  a  well-defined  spot  was  known 
to  remain  long  enough  on  Saturn  to  determine  the  period  of 
its  rotation  was  in  the  time  of  Sir  W.  Herschel,  who,  from 
observations  extending  over  several  weeks,  found  the  time  of 


THE  RINGS  OF  SATURN.  349 

rotation  to  be  10  hours  16  minutes.*  No  furtlier  opportu- 
nity for  determining  this  period  seems  to  have  offered  itself 
until  1876,  when  an  appearance  altogether  new  suddenly 
showed  itself  on  the  globe  of  this  planet.  On  the  evening  of 
December  7th,  1876,  Professor  Hall,  who  had  been  engaged 
in  measures  of  the  satellites  of  Saturn  with  the  great  Wash- 
ington telescope,  saw  a  brilliant  white  spot  near  the  equator 
of  the  planet.  It  seemed  as  if  an  immense  eruption  of  white- 
hot  matter  had  suddenly  burst  up  from  the  interior.  The 
spot  gradually  spread  itself  out  in  the  direction  which  would 
be  east  on  the  planet,  so  as  to  assume  the  form  of  a  long  light 
streak,  of  which  the  brightest  point  was  near  the  following 
end.  It  continued  visible  until  January,  when  it  became  faint 
and  ill-defined,  and  the  planet  was  lost  in  the  rays  of  the  sun. 
Immediately  upon  the  discovery  of  this  remarkable  phenom- 
enon, messages  were  sent  to  other  observers  in  various  parts  of 
the  country,  and  on  the  10th  it  was  seen  by  several  observers, 
who  noted  the  time  at  Avliich  it  crossed  the  centre  of  the  disk 
in  consequence  of  the  i-otation  of  the  planet.  From  all  the 
observations  of  this  kind,  Professor  Hall  found  the  period  of 
Saturn  to  be  10  hours  14  minutes,  taking  the  brightest  part 
of  the  streak,  which,  as  we  have  said,  was  near  one  end. 
Had  the  middle  of  the  streak  been  taken,  the  time  would  have 
been  less,  because  the  bright  matter  seemed  to  be  carried 
along  in  the  direction  of  the  planet's  rotation.  Attributing 
this  to  a  wind,  the  velocity  of  the  latter  would  have  been  be- 
tween 50  and  100  miles  an  hour. 

§  4.  The  Rings  of  Saturn. 

The  most  extraordinary  feature  of  Saturn  is  the  magnificent 
system  of  rings  by  which  he  is  surrounded.  To  the  early 
telescopists,  who  could  not  command  sufficient  optical  power 
to  see  exactly  what  it  was,  this  feature  was  a  source  of  great 

*  It  is  very  curious  that  nearly  all  modern  writers  give  about  10  hours  29  min- 
utes as  the  time  of  rotation  of  Saturn  which  Herschel  finally  deduced.  I  can 
find  no  such  result  in  Herschel's  papers.  A  suspicious  coincidence  is  that  this 
period  agrees  with  that  assigned  for  the  time  of  rotation  of  the  ring. 


350  THE  LOLAR  SYSTEM. 

perplexity  and  difference  of  opinion.  To  Galileo  it  made  the 
planet  appear  triform — a  large  globe  with  two  small  ones  af- 
fixed to  it,  one  on  each  side.  After  he  had  observed  it  for  a 
year  or  two,  he  was  greatly  perplexed  to  find  that  the  append- 
ages had  entirely  disappeared,  leaving  Satnrn  a  single  round 
globe,  like  the  otlier  planets.  His  chagrin  was  heightened  by 
the  fear,  not  unnatural  under  the  circumstances,  that  the  curi- 
ous form  he  had  before  seen  might  be  due  to  some  optical  il- 
lusion connected  with  his  telescope.  It  is  said  (I  do  not  know 
on  what  authority)  that  his  annoyance  at  the  supposed  decep- 
tion into  which  he  had  fallen  was  so  great  that  he  never  again 
looked  at  Saturn. 

A  very  few  years  sufficed  to  show  other  observers,  who  had 
command  of  more  powerful  telescopes,  that  the  singularity  of 
form  was  no  illusion,  but  that  it  varied  from  time  to  time. 
We  give  several  pictures  from  Huyghens's  Systema  Saturniumy 
showing  how  it  was  represented  b}'  various  observers  during 
the  fii"st  forty  yeai-s  of  the  telescope.  If  the  reader  will  com- 
pare these  with  the  picture  of  Saturn  and  his  rings  as  they 
actually  are.  he  will  see  how  near  many  of  the  observer  came 
to  a  representation  of  the  proper  apparent  form,  though  none 
divined  to  what  sort  of  an  appendage  the  appearance  was 
due. 

The  man  who  at  last  solved  the  riddle  was  Huyghens,  of 
whose  long  telescopes  we  have  already  spoken.  Examining 
Satuin  in  March  and  April,  1655,  he  saw  that  instead  of  the 
appendages  presenting  the  appearance  of  curved  handles,  as 
in  previous  years,  a  long  narrow  arm  extended  straight  out  on 
each  side  of  the  planet.  The  spring  following,  this  arm  had 
disappeared,  and  the  planet  appeared  perfectly  round  as  Gal- 
ileo had  seen  it  in  1612.  In  October,  1656,  the  handles  had 
reappeared,  much  as  he  had  seen  them  a  year  and  a  half  be- 
fore. To  his  remarkably  acute  mathematical  and  mechanical 
mind  this  mode  of  disappearance  of  the  handles  sufficed  to 
suggest  the  cause  which  led  to  their  apparent  form.  "Waiting 
for  entire  confirmation  by  future  observations,  he  communica- 
ted his  theory  to  his  fellow-astronomers  in  the  following  com- 


THE  RINGS  OF  SATUIiX. 


351 


Pio.  89. — Specimens  of  drawings  of  Saturn  by  various  observers  before  tlie  rincjs  were 
recognized  as  such :  I.  Form  us  given  by  Galileo  in  1610 ;  II.  Drawing  by  Scheinev,  in 
1614,  "showing  ears  to  Saturn;"  III.  Drawing  by  Ricciolus,  in  1640  and  1643;  IV., V., 
VI.,  and  VII.  are  by  Ilevelius,  and  show  the  changes  due  to  the  different  angles  under 
which  the  rings  were  seen  ;  VIII.  and  IX.  are  by  Ricciolns,  between  1G4S  and  1650, 
when  the  ring  was  seen  at  the  greatest  angle ;  X.  is  by  a  Jesuit  who  passed  nnder 
the  pseudonym  of  Eiistarkiuit  de  Divinia;  XI.  is  by  Foutana;  XII.  by  Gasseudi  and 
Blancanus,  and  XIII.  by  Ricciolus. 

bination  of  letters,  printed  without  explanation  at  the  end  of  a 
little  pamphlet  on  his  discovery  of  the  satellite  of  Saturn : 

aaaaaaa  ccccc  d  eee.ee  g  h  iiiiiii  Ull  mm  nnnnnnnnn  oooo  pp  q  rr  s  ttttt  uuuuu, 

which,  properly  arranged,  read — 

^*  Anmilo  cingitur,  tenui,  piano,  nusqunm  coh(trente,  ad  eclipticam  inrJinato" 
(It  is  girdled  by  a  thin  piano  ring,  nowhere  touching,  inclined  to  the  ecliptic). 

This  description  is  remarkably  complete  and  accurate ;  and 
enabled  Huyghens  to  give  a  satisfactory  explanation  of  the 

24 


352  THE  SOLAR  SYSTEM. 

various  phases  which  the  ring  had  assumed  as  seen  from  the 
earth.  Owing  to  the  extreme  thinness  and  flatness  of  the  ob- 
ject, it  was  completely  invisible  in  the  telescopes  of  that  time 
when  its  edge  was  presented  towards  the  observer  or  towards 
the  sun.  This  happens  twice  in  each  revolution  of  Saturn,  in 
much  the  same  way  that  the  earth's  equator  is  twice  directed 
towards  the  sun  in  the  course  of  the  year.  The  ring  is  in- 
clined to  the  plane  of  the  planet's  orbit  by  27°,  corresponding 
to  the  angle  of  23^°  between  the  earth's  ecpiator  and  the 
ecliptic.  The  general  aspect  from  the  earth  is  very  near  the 
same  as  from  the  sun.  As  the  planet  revolves  around  the 
sun,  the  axis  and  plane  of  tlie  ring  preserve  the  same  absolute 
direction  in  space,  just  as  the  axis  of  the  earth  and  the  plane 
of  the  equator  do. 

"When  the  planet  is  in  one  part  of  its  orbit,  an  observer  at 
the  sun  or  on  the  earth  will  see  the  upper  or  northern  side  of 
the  rinoj  at  an  inclination  of  27°.  This  is  the  s^reatest  anorle 
at  which  the  ring  can  ever  be  seen,  the  position  occurring 
when  the  planet  is  in  262°  of  longitude,  in  the  constellation 
Sagittarius.  When  the  planet  has  moved  through  a  quarter 
of  a  revolution,  the  edge  of  the  ring  is  turned  towai'ds  the  sun, 
and,  owing  to  its  extreme  thinness,  it  is  visible  only  in  the 
most  powerful  telescopes  as  an  exceedingly  fine  line  of  light, 
stretching  out  on  each  side  of  the  planet.  In  this  position  the 
planet  is  in  longitude  352°,  in  the  constellation  Pisces.  AYhen 
the  planet  has  moved  90°  farther,  an  observer  on  the  sun  or 
earth  again  sees  the  ring  at  an  angle  of  27° ;  but  now  it  is  the 
lower  or  southern  side  which  is  visible.  The  planet  is  now  in 
longitude  82°,  between  the  constellations  Taurus  and  Gemini. 
When  it  has  moved  90°  farther,  to  longitude  172°,  in  the  con- 
stellation Leo,  the  edge  of  the  ring  is  again  turned  towards 
the  earth  and  sun. 

Thus  there  are  a  pair  of  opposite  points  of  the  orbit  of  Sat- 
urn in  Avhich  the  rings  are  turned  edgewise  to  us,  and  another 
pair  half-way  between  the  first  in  Avhich  the  ring  is  seen  at 
its  maximum  inclination  of  about  27°.  Since  the  planet  per- 
forms a  revolution  in  29^-  years,  these  phases  occur  at  average 


THE  EINGS  OF  SATURN.  353 

intervals  of  about  seven  years  and  four  months.  The  follow- 
ing are  some  of  the  times  of  their  occurrence : 

1870.  The  planet  being  between  Scorpio  and  Sagittarius, 
the  ring  was  seen  open  to  its  greatest  breadth,  the  north  side 
being  visible.     The  same  phase  recurs  at  the  end  of  1899. 

1878  (February  7th).  The  edge  of  the  ring  was  turned  to- 
wards the  Sim,  so  that  only  a  thin  line  of  light  was  visible. 
The  planet  was  then  between  Aquarius  and  Pisces. 

1885.  The  planet  being  in  Taurus  (the  Bull)  the  south  side 
of  the  rings  was  seen  at  tlie  greatest  elevation. 

1892.  The  edge  of  the  ring  is  again  turned  towards  the  sun, 
the  planet  being  in  Leo  (the  Lion). 

Owing  to  the  motion  of  the  earth,  the  times  when  the  edge 
of  the  ring  is  turned  towards  it  do  not  accurately  correspond 
to  those  when  it  is  turned  towards  the  sun,  and  the  points  of 
Saturn's  orbit  in  which  this  may  occur  range  over  a  space  of 
several  degrees.  The  most  interesting  times  for  viewing  the 
rings  with  powerful  telescopes  are  on  those  rare  occasions 
when  the  sun  shines  on  one  side  of  the  ring,  while  the  dark 
side  is  directed  towards  the  earth.  On  these  occasions  the 
plane  of  the  ring,  if  extended  out  far  enough,  would  pass  be- 
tween the  sun  and  tlie  eartli.  This  was  the  case  between  Feb- 
ruary 9th  and  March  1st,  1878  ;  but,  unfortunately,  at  that  titne 
the  earth  and  Saturn  were  on  opposite  sides  of  the  sun,  so  that 
the  planet  was  nearly  lost  in  the  sun's  rays,  and  could  be  ob- 
served only  low  down  in  the  west  just  after  sunset.  In  1891 
the  position  of  Saturn  will  be  almost  equally  unfavorable  for 
the  observation  in  question,  as  it  can  be  made  only  in  the  early 
mornings  of  the  latter  part  of  October  of  that  year,  just  after 
Saturn  has  risen.  In  fact,  a  good  opportunity  will  not  occur 
till  1907.  In  northern  latitudes  the  finest  telescopic  views  of 
Saturn  and  his  ring  may  be  obtained  between  1881  and  1889, 
because  during  that  interval  Saturn  passes  his  perihelion,  and 
also  the  point  of  greatest  northern  declination,  while  the  ring 
is  opened  out  to  its  widest  extent.  In  fact,  these  three  most 
favorable  conditions  all  fall  nearly  together  during  the  years 
1881-'S5. 


354  THE  SOLAR  SYSTEM. 

After  Iluyghens,  the  next  step  forward  in  discoveries  on 
Saturn's  ring  was  made  by  Cassini  of  Paris,  who  found  in  1675 
that  there  were  really  two  rings,  divided  by  a  narrow  dark 
line,  now  commonly  called  Cassini's  division.  The  breadth  of 
the  rings  is  very  unequal,  the  itmer  ring  being  several  times 
broader  than  the  outer  one.  A  moderate  -  sized  telescope  is 
sufficient  to  show  this  division  near  the  extreme  points  of  the 
ring  if  the  atmosphere  is  steady  but  it  requires  both  a  large 
telescope  and  tine  seeing  to  trace  it  all  the  way  across  that 
part  of  the  ring  which  is  between  the  observer  and  the  ball  of 
the  planet.  Other  divisions,  especially  in  the  outer  ring,  have 
at  times  been  suspected  by  various  observei-s,  but  if  they  real- 
ly existed,  they  must  have  been  only  temporary,  forming  and 
closing  up  again. 

In  December,  1850,  the  astronomical  world  was  surprised 
by  the  announcement  that  Professor  Bond,  of  Cambridge,  had 
discovered  a  third  ring  to  Saturn.  It  lay  between  the  rings 
already  known  and  the  planet,  being  joined  to  the  inner  edge 
of  the  inner  ring.  It  had  the  appearance  of  a  ring  of  crape, 
being  so  dark  and  obscure  that  it  might  easily  have  been 
overlooked  in  smaller  telescopes.  It  was  seen  in  England  by 
Messrs.  Lassell  and  Dawes  before  it  was  formally  announced 
by  the  Bonds.  Something  of  the  kind  had  been  seen  by  Dr. 
Galle,  at  Berlin,  as  far  back  as  1838;  but  the  paper  on  the 
subject  by  Encke,  the  director  of  the  observiitory,  did  not  de- 
scribe the  appearance  very  clearl3\  Indeed,  on  examining  the 
descriptions  of  observers  in  the  early  part  of  the  eighteenth 
century,  some  reason  is  found  for  suspecting  that  they  saw 
this  dusky  ring;  but  none  of  the  descriptions  are  sufficiently 
definite  to  establish  the  fact,  though  it  is  strange  if  an  object 
30  plain  as  this  ring  now  is  should  have  been  overlooked  by 
all  the  older  observers. 

The  question  whether  changes  of  various  sorts  are  going  ou 
in  the  rings  of  Saturn  is  one  which  is  still  unsettled.  There 
is  some  reason  to  believe  that  the  supposed  additional  divis- 
ions noticed  in  the  rings  from  time  to  time  are  only  errors  of 
vision,  due  partly  to  the  shading  which  is  known  to  exist  on 


THE  RINGS  OF  SATURN.  355 

various  parts  of  the  ring.  By  reference  to  the  diagram  of 
Saturn,  it  will  be  seen  that  the  outer  ring  has  a  shaded  line 
extending  around  it  about  two-thirds  of  the  way  from  its  in- 
ner to  its  outer  edge.  This  line,  however,  is  not  fine  and 
sharp,  like  the  known  division,  but  seems  to  shade  off  gradual- 
ly towards  each  edge.  As  observers  who  have  supposed  them- 
feelves  to  see  a  division  in  this  ring  saw  it  where  this  shaded 
line  is,  and  do  not  speak  of  the  latter  as  anything  distinct 
from  the  former,  there  is  reason  to  believe  that  they  mistook 
this  permanent  shading  for  a  new  division.  The  inner  ring  is 
brightest  near  its  outer  edge,  and  shades  off  gradually  towards 
its  inner  edge.  Here  the  dusky  ring  joins  itself  to  it,  and  ex- 
tends about  half-w'ay  in  to  the  planet. 

As  seen  with  the  great  Washington  equatorial  in  the  au- 
tumn of  1874,  there  was  no  great  or  sudden  contrast  be- 
tween the  inner  or  dark  edge  of  the  bright  ring  and  the  out- 
er edge  of  the  dusky  ring.  There  M'as  some  suspicion  that 
the  one  shaded  into  the  other  by  insensible  gradations.  ISTo 
one  could  for  a  moment  suppose,  as  some  observers  have,  that 
there  was  a  separation  between  these  two  rings.  All  these 
considerations  give  rise  to  the  question  whether  the  dusky 
ring  may  not  be  growing  at  the  expense  of  the  inner  bright 
ring. 

A  most  startling  theory  of  changes  in  the  rings  of  Saturn 
was  propounded  by  Struve,  in  1851.  This  was  nothing  less 
than  that  the  inner  edge  of  the  ring  was  gradually  approach- 
ing the  planet  in  consequence  of  the  w'hole  ring  spreading  in- 
wards, and  tlie  central  o^^ening  thus  becoming  smaller.  The 
data  on  which  this  theory  was  founded  were  the  descriptions 
and  drawings  of  the  rings  by  the  astronomers  of  the  seven- 
teenth century,  especially  Huyghens,  and  the  measures  ex- 
ecuted by  later  astronomers  up  to  the  time  at  which  Struve 
wrote.  The  rate  at  which  the  space  between  the  ring  and  the 
planet  was  diminishing  seemed  to  be  about  1".3  per  century. 
The  following  are  the  numbers  used  by  Struve,  Avhicli  are  de- 
duced from  the  descriptions  by  the  ancient  observers,  and  the 
measures  by  the  modern  ones : 


356  THE  SOLAR  SYSTEM. 


Huyghens 

Huyghens  and  Cassini 

Bradley 

Herschel 

W.  Struve 

Encke  and  Galle 

Otto  Struve 


1657 
1695 
1719 
1799 
1826 
1838 
1851 


Distance  between 
Rin2  and  Planet. 


6.5 

6.0 

6.4 

5.12 

4.36 

4.04 

3.67 


Breadth  of 
Ring. 


4.6 

5.1 

5.7 

5.98 

6.74 

7.06 

7.43 


If  these  estimates  and  measures  were  certainly  accurate, 
they  would  place  the  fact  of  a  progressive  approach  of  the 
rings  to  the  ball  beyond  doubt,  an  approach  which,  if  it  con- 
tinued at  the  same  rate,  would  bring  the  inner  edge  of  the 
ring  into  contact  with  the  planet  about  the  year  2150.  But 
in  measuring  such  an  object  as  the  inner  edge  of  the  ring  of 
Saturn,  which,  as  we  have  just  said,  seems  to  fade  gradually 
into  the  obscure  ring,  different  observers  will  always  obtain 
different  results,  and  the  differences  among  the  four  observ- 
ers commencing  with  W.  Struve  are  no  greater  than  are  often 
seen  in  measuring  an  object  of  such  uncertain  outline.  Hence, 
considering  the  great  improbability  of  so  stupendous  a  cosmi- 
cal  change  going  on  with  so  much  rapidity,  Struve's  theory  has 
always  been  viewed  with  doubt  by  other  astronomers. 

At  the  same  time,  it  is  impossible  to  reconcile  the  descrip- 
tions by  the  early  observers  with  the  obvious  aspect  of  the 
ring  as  seen  now  without  supposing  some  change  of  the  kind. 
The  most  casual  observer  who  now  looks  at  Saturn  will  see 
that  the  breadth  of  the  two  bright  rings  together  is  at  least 
half  as  great  again,  if  not  twice  as  great,  as  that  of  the  dark 
space  between  the  inner  edge  of  the  bright  ring  and  the  plan- 
et. But  Huj'ghens  describes  the  dark  space  as  about  equal 
to  the  breadth  of  the  ring,  or  a  little  greater.  Supposing  the 
rino-  the  same  then  as  now,  could  this  error  have  arisen  from 
ihe  imperfection  of  his  telescope  ?  No ;  because  the  effect  of 
the  imperfection  would  have  been  directly  the  opposite.  The 
old  telescopes  all  represented  planets  and  other  bright  objects 
too  large,  and  therefore  would  show  dark  spaces  too  small, 
owing  to  the  irradiation  produced  by  their  imperfect  glasses. 
A  strong  confirmation  of  Struve's  view  is  found  in  the  old 


CONSTITUTION  OF  THE  RING.  357 

pictures  given  in  Fig.  89  by  those  observers  who  conld  not 
clearly  make  out  the  ring.  In  nearly  all  cases  the  dark  spaces 
were  more  conspicuous  than  the  edges  of  the  ring.  But  it 
we  now  look  at  Saturn  tlirough  a  very  bad  atmosphere,  though 
the  elliptical  outline  of  the  ring  may  be  clearly  made  out, 
the  dark  space  will  be  almost  obliterated  by  the  encroachment 
of  the  light  of  the  planet  and  ring  upon  it.  The  question  is, 
therefore,  one  of  those  the  complete  solution  of  which  must 
be  left  to  future  observers. 

§  5.  Constitution  of  the  Ring. 

The  difficulties  which  investigators  have  met  with  in  ac- 
counting; for  the  rings  of  Saturn  are  of  the  same  nature  as 
those  we  have  described  as  arising  from  spectroscopic  discov- 
eries respecting  the  envelopes  of  the  sun.  They  illustrate  the 
philosophic  maxim  that  surprise — in  which  term  we  may  in- 
clude all  difficulty  and  perplexity  which  men  meet  with  in 
seeking  to  account  for  the  phenomena  of  nature — is  a  result 
of  partial  knowledge,  and  cannot  exist  either  with  entire  ig- 
norance or  complete  knowledge.  Those  who  are  perfectly 
ignorant  are  surprised  at  nothing,  because  they  expect  noth- 
ing, while  perfect  knowledge  of  what  is  to  happen  also  pre- 
cludes the  same  feeling.  The  astronomers  of  two  centuries 
ago  saw  nothing  surprising  in  the  fact  of  a  pair  of  rings  sur- 
rounding a  planet,  and  accompanying  it  in  its  orbit,  because 
they  were  not  acquainted  with  the  effects  of  gravitation  on 
such  bodies  as  the  rings  seemed  to  be.  But  when  Laplace  in- 
vestigated the  subject,  he  found  that  a  homogeneous  and 
uniform  ring  surrounding  a  planet  could  not  be  in  a  state 
of  stable  equilibrium.  Let  it  be  balanced  ever  so  nicely,  the 
slightest  external  force,  the  attraction  of  a  satellite  or  of  a 
distant  planet,  would  destroy  the  equilibrium,  and  the  ring 
would  soon  be  precipitated  upon  the  planet,  lie  therefore 
remarked  that  the  rings  must  have  irregularities  in  their 
form,  such  as  Ilerschel  supposed  he  had  seen;  but  he  did 
not  investigate  the  question  whetlier  with  those  irregularities 
the  equilibrium  would  really  be  stable. 


358  THE  SOLAR  SYSTEM. 

The  question  was  next  taken  up  in  this  country  by  Profess- 
ors  Peirce  and  Bond.  The  latter  started  from  the  supposed 
result  of  observations  —  that  new  divisions  show  themselves 
from  time  to  time  in  the  ring,  and  then  close  up  again.  He 
thence  inferred  that  the  rings  must  be  fluid,  and,  to  confirm 
this  view,  he  showed  the  impossibility  of  even  an  irregular 
solid  pair  of  rings  fulfilling  all  the  necessary  conditions  of 
stability  and  freedom  of  motion.  Professor  Peirce,  taking  up 
the  same  subject  from  a  mathematical  point  of  view,  found 
that  no  conceivable  form  of  irregular  solid  ring  would  be  in  a 
state  of  stable  equilibrium;  he  therefore  adopted  Bond's  view 
that  the  rings  were  fluid.  Following  up  the  investigation, 
he  found  that  even  a  fluid  ring  would  not  be  entirely  stable 
without  some  external  support,  and  he  attributed  that  support 
to  the  attractions  of  the  satellites.  But  as  Laplace  did  not 
demonstrate  that  irregularities  would  make  the  ring  stable,  so 
Peirce  merely  fell  back  upon  the  attraction  of  the  satellites  as 
a  sort  of  forlorn  hope,  but  did  not  demonstrate  that  the  fluid 
ring  would  really  be  stable  under  the  influence  of  their  attrac- 
tion. Indeed,  it  now  seems  very  doubtful  whether  this  at- 
traction would  have  the  effect  supposed  by  Peirce. 

The  next,  and,  we  may  say,  the  last,  important  step  was 
taken  by  Professor  J.  Clerk  Maxwell,  of  England,  in  the 
Adams  prize  essay  for  1856.  lie  brought  forward  objections 
which  seem  unanswerable  against  both  the  solid  and  the  fluid 
ring,  and  revived  a  theory  propounded  by  Cassini  about  the 
beginning  of  the  last  century.*  This  astronomer  considered 
the  ring  to  be  formed  by  a  cloud  of  satellites,  too  small  to 
be  separately  seen  in  the  telescope,  and  too  close  together  to 
admit  of  the  intervals  between  them  being  visible.  This  is 
the  view  of  the  constitution  of  the  rings  of  Saturn  now  most 
generally  adopted.  The  reason  M'hy  the  ring  looks  solid  and 
continuous  is  that  the  satellites  are  too  small  and  too  numerous 
to  be  seen  singly.     They  are  like  the  separate  little  drops  of 


*  See  Memoirs  of  the  French  Academy  of  Sciences  for  1715,  p.  47;  or  Cas- 
Bini's  "Semens  d'Astronomie,"i).  338,  Paris,  1740. 


THE  SATELLITES  OF  SATURN.  359 

water  of  which  clouds  and  fog  are  composed,  which,  to  our 
eyes,  seem  like  solid  masses.  In  the  dusky  ring  tlie  particles 
may  be  so  scattered  that  we  can  see  through  the  cloud,  the 
reason  that  it  looks  dusky  being  simply  the  comparatively 
small  number  of  the  particles,  so  that  to  the  distant  eye  they 
appear  like  the  faint  stippling  of  an  engraving. 

The  question  arises  whether  the  comparative  darkness  of 
some  portions  of  the  bright  ring  may  not  be  due  to  the  paucity 
of  the  particles,  which  allows  the  dark  background  of  the  sky 
to  be  seen  through.  This  question  cannot  be  positively  an- 
swered until  further  observations  are  made ;  but  the  prepon- 
derance of  evidence  favors  the  view  that  the  entire  bright 
ring  is  opaque,  and  that  the  dark  shading  is  due  entirely  to  a 
darker  color  of  that  part  of  the  ring.  Indeed,  for  anything 
we  certainly  know,  the  whole  ring  may  be  continuous  and 
opaque,  the  darker  shade  of  some  parts  arising  solely  from  the 
particles  being  there  black  in  color.  The  only  Avay  to  settle 
conclusively  the  questions  whether  these  parts  of  the  ring  look 
black,  owing  to  the  sky  beyond  showing  through  openings,  as 
it  were,  or  from  a  black  color  of  the  ring,  is  to  find  whether  a 
star  or  other  object  can  be  seen  through  the  dark  spaces.  Jjut 
an  opportunity  for  seeing  a  bright  star  through  the  ring  has 
never  yet  presented  itself.  The  most  obvious  way  of  settling 
the  question  in  respect  to  the  dusky  ring  is  to  notice  whether 
the  planet  itself  can  be  seen  through  it ;  but  this  is  much  more 
difficult  than  might  be  supposed,  owing  to  the  ill -defined  as- 
pect of  the  ring.  The  testimony  of  both  Lassell  and  Trouve- 
lot  is  in  fa\'or  of  the  view  that  this  ring  is  partially  transpar- 
ent ;  but  their  observations  will  need  to  be  repeated  when  the 
ring  is  opened  out  to  our  sight  after  1882. 

§  6.  The  Satellites  of  Saturn. 

When  Huyghens  commenced  his  observations  of  Saturn  in 
1655,  he  saw  a  star  near  the  planet  which  a  few  days'  observa- 
tion enabled  him  to  recognize  as  a  satellite  revolving  round  it 
in  about  fifteen  days.  In  his  "  Systema  Saturm'um,'^  he  vent- 
ured to  express  the  opinion  that  this  discovery  completed  the 


360 


THE  SOLAR  SYSTEM. 


solar  system,  wliicl I  now  comprised  six  planets  (Saturn  being 
then  the  outermost  known  planet)  and  six  satellites  (one  of 
the  earth,  four  of  Jupiter,  and  this  one  of  Saturn),  making 
the  perfect  number  of  twelve.  He  was,  therefore,  contident 
that  no  more  satellites  were  left  to  discover,  and  through  fail- 
ing to  search  for  others,  he  probably  lost  the  honor  of  addi- 
tional discoveries. 

Twelve  years  after  this  prediction,  Cassini  discovered  a  sec- 
ond satellite  outside  that  found  by  Huyghens,  and  within  a 
few  years  more  he  found  three  others  inside  of  it.  The  dis- 
covery of  four  satellites  by  one  astronomer  was  so  brilliant  a 
result  of  French  science  that  tlie  Government  of  France 
struck  a  medal  in  commemoration  of  it,  bearing  the  iuscrip- 
tion  Saturni  Satellites  primum  cogniti.  These  five  satellites 
completed  the  number  known  for  more  than  a  century.  In 
17S9  Herschel  discovered  two  new  ones  still  nearer  the  ring 
than  those  found  by  Cassini.  The  space  between  the  ring  and 
the  inner  one  is  so  small  that  the  satellite  is  generally  invisible, 
even  in  the  most  powerful  telescopes.  Finally,  in  September, 
1S4S,  the  Messi-s.  Bond,  at  the  Observatory  of  Harvard  Col- 
lege, found  an  eighth  satellite,  while  examining  the  ring  of 
Saturn.  By  a  singular  coincidence,  this  satellite  Avas  found  by 
Mr.  Lassell,  of  England,  only  a  couple  of  nights  after  it  was 
detected  by  the  Bonds.  The  names  which  have  been  given  to 
these  bodies  are  shown  in  the  following  list,  in  which  the  sat- 
ellites are  arranged  in  the  order  of  their  distance  from  the 
planet.  The  distances  are  given  in  semidiameters  of  Saturn. 
More  exact  elements  will  be  found  in  the  Api^endix  to  this 
.olume. 


Xame. 

Planet. 

Discoverer. 

Date. 

1 

Mimas 

3.3 

Herschel. . 

1789,  September  17th. 

2 

Enceladus. 

4.3 

Herschel. . 

1789,  August  28th. 

3 

Tethvs 

.5.3 

Cassini .... 

1684,  March. 

4 

Dione 

6.8 

Cassini 

168 1,  March. 

5 

Rliea 

9.5 

Cassini 

1672,  December  23d. 

6 

Titan 

20.7 

Huvghens. 

165.5,  March  25th. 

7 

Hvperion . 

26.8 

Bond 

1848,  September  16th. 

8 

Japetus.... 

64.4 

Cassini .... 

1671,  October. 

UEANUS  AND  ITS  SATELLITES.  361 

The  brightness,  or  rather,  the  visibihtj,  of  these  satellites 
follows  the  same  order  as  their  discovery.  The  smallest  tel- 
escope will  show  Titan,  and  one  of  very  moderate  size  will 
show  Japetus  in  the  western  part  of  its  orbit.  Four  or  five 
inches  aperture  will  show  Rhea,  and  perhaps  Tethys  and  Di- 
one,  while  seven  or  eight  inches  are  required  for  Enceladus, 
and  even  with  that  aperture  it  will  probably  be  seen  only  near 
its  greatest  elongation  from  the  planet.  Mimas  can  be  seen 
only  near  the  same  position,  unless  the  ring  is  seen  edgewise, 
and  will  then  require  a  large  telescope,  probably  twelve  inches 
or  upwards.  Finally,  Hyperion  can  be  recognized  only  with 
the  most  powerful  telescopes,  not  only  on  account  of  its  faint- 
ness,  but  of  the  difficulty  of  distinguishing  it  from  minute  stars. 

All  these  satellites,  except  Japetus,  revolve  very  nearly  in 
the  plane  of  the  ring.  Consequently,  when  the  edge  of  the 
ring  is  turned  towards  the  earth,  the  satellites  seem  to  swing 
from  one  side  of  the  planet  to  the  other  in  a  straight  line,  run- 
ning along  the  thin  edge  of  the  ring,  like  beads  on  a  string. 
This  phase  affords  the  best  opportunity  of  seeing  the  inner 
satellites  Mimas  and  Enceladus,  because  they  are  no  longer 
obscured  by  the  brilliancy  of  the  ring. 

Japetus,  the  outer  satellite  of  all,  exhibits  this  remarkable 
peculiarity,  that  while  in  one  part  of  its  orbit  it  is  the  bright- 
est of  the  satellites,  except  Titan,  in  the  opposite  part  it  is  al- 
most as  faint  as  Hyperion,  and  can  be  seen  only  in  large 
telescopes.  When  west  of  the  planet,  it  is  bright ;  when  east 
of  it,  faint.  Tliis  peculiarity  has  been  accounted  for  only  by 
supposing  that  the  satellite,  like  our  moon,  always  presents 
the  same  face  to  the  planet,  and  that  one  side  of  it  is  white 
and  the  other  intensely  black.  The  only  difficulty  in  the  way 
of  this  explanation  is  that  it  is  doubtful  whether  any  known 
substance  is  so  black  as  one  side  of  the  satellite  must  be  to 
account  for  such  great  changes  of  brilliancy. 

§  7.  Uranus  and  its  Satellites. 

Uranus,  the  next  planet  beyond  Saturn,  is  at  a  mean  dis- 
tance from  the  sun  of  about  1770  millions  of  miles,  and  per- 


362  THE  SOLAB  SYSTEM. 

forms  a  revolution  in  84  years.  It  shines  as  a  star  of  the  sixth 
magnitude,  and  can  therefore  be  seen  with  the  naked  eye,  if 
one  knows  exactly  where  to  look  for  it.  It  was  in  opposition 
February  20th,  1879,  and  the  time  of  opposition  during  the 
remainder  of  the  present  century  may  be  found  by  adding  4-J 
days  for  every  year  subsequent  to  1879.  To  find  it  readily, 
either  with  a  telescope  or  the  naked  eye,  recourse  must  be  had 
to  the  Nautical  Almanac,  where  the  position  (right  ascension 
and  declination)  is  given  for  each  day  in  the  year. 

Of  course  the  smallest  telescopes  will  show  this  planet  as  a 
star,  but  to  recognize  its  disk  a  magnifying  power  of  at  least 
100  should  be  used,  and  200  will  be  necessary  to  any  one  who 
is  not  a  practised  observer.  As  seen  in  a  large  telescope,  the 
planet  has  a  decided  sea-green  color.  Very  faint  markings 
have  been  seen  on  the  disk  by  Professor  Young,  though  no 
changes  due  to  an  axial  rotation  could  be  established ;  but  it 
may  be  regarded  as  certain  that  it  does  rotate  in  the  same 
plane  in  which  the  satellites  revolve  around  it. 

Discovery  of  Uranus. —  This  planet  was  discovered  by  Sir 
William  Herschel,  in  March,  1781.  Perceiving  by  its  disk 
that  it  was  not  a  star,  and  by  its  motion  that  it  was  not  a  neb- 
ula, he  took  it  for  a  comet.  The  possibility  of  its  being  a  new 
planet  did  not  at  first  occur  to  him ;  and  he  therefore  com- 
municated his  discovery  to  the  Royal  Society  as  being  one  of 
a  new  comet.  Various  computing  astronomers  thereupon  at- 
tempted to  find  the  orbit  of  the  supposed  comet,  from  the  ob- 
servations of  Herschel  and  others,  assuming  it  to  move  in  a 
parabola,  like  otlier  comets.  But  the  actual  motion  of  the 
body  constantly  deviated  from  the  orbits  thus  computed  to 
such  an  extent  that  new  calculations  had  to  be  repeatedly 
made.  After  a  few  weeks  it  was  found  that  if  it  moved  in  a 
parabola,  the  nearest  distance  to  the  sun  must  be  at  least  four- 
teen times  that  of  the  earth  from  the  sun,  a  perihelion  distance 
many  times  greater  than  that  of  any  known  comet.  This  an- 
nouncement gave  the  hint  that  some  other  hypothesis  nmst  be 
resorted  to,  and  it  was  then  found  that  all  the  observations 
could  be  well  represented  by  a  circular  orbit,  with  a  radius 


URANUS  AND  ITS  SATELLITES.  363 

nineteen  times  that  of  the  earth's  orbit.  The  object  was,  there- 
fore,  a  planet  moving  at  double  the  distance  of  Saturn. 

With  a  commendable  feeling  of  gratitude  towards  the  royal 
patron  who  had  afforded  him  the  means  of  making  his  dis- 
coveries, Ilerschel  proposed  to  call  the  new  planet  Georgium 
Sidus  (the  Star  of  the  Georges).  This  name,  contracted  to  "  the 
Georgian,"  was  employed  in  England  until  1850,  but  never 
came  into  use  on  the  Continent.  Lalande  thought  the  most 
appropriate  name  of  the  planet  was  that  of  its  discoverer,  and 
therefore  proposed  to  call  it  Herschel.  But  this  name  met 
with  no  more  favor  than  the  other.  Several  other  names  were 
proposed,  but  that  of  Uranus  at  length  met  with  universal 
adoption.  It  was  proposed  by  Bode  as  the  most  appropriate, 
on  the  ground  that  the  most  distant  body  of  our  system  might 
be  properly  nanied  after  the  oldest  of  the  gods. 

After  the  elliptic  orbit  of  the  planet  had  been  accurately 
computed,  and  its  path  mapped  out  in  the  heavens,  it  was 
found  that  it  had  been  seen  a  surprising  number  of  times  as  a 
star  without  the  observers  having  entertained  any  suspicion  of 
its  planetary  nature.  It  had  passed  through  the  field  of  their 
telescopes,  and  they  had  noted  the  time  of  its  transit,  or  its 
declination,  or  both,  but  had  entered  it  in  their  journals  simply 
as  an  unnamed  star  of  the  constellation  in  which  it  happened 
to  be  at  the  time.  It  had  been  thus  seen  five  times  by  Flam- 
8teed,  the  first  observation  being  in  1690,  nearly  a  century  be- 
fore the  discovery  by  Herschel.  What  is  most  extraordina- 
ry, it  had  been  observed  eight  times  in  rapid  succession  by 
Le  Monnier,  of  Paris,  in  December,  1768,  and  January,  1769. 
Had  that  astronomer  merely  taken  the  trouble  to  reduce  and 
compare  his  observations,  he  would  have  anticipated  Herschel 
by  twelve  years.  Indeed,  considering  how  easily  the  planet 
can  be  seen  with  the  naked  eye,  it  is  illustrative  of  the  small 
amount  of  care  devoted  to  cataloo-uino-  the  stars  that  it  was 
not  discovered  without  a  telescope. 

Satellites  of  Uranus.  —  In  January  and  February,  1787, 
Herschel  found  that  Uranus  was  accompanied  by  two  satel- 
lites, of  which  the  inner  performed  a  revolution  in  a  little  less 


364  THE  SOLAR  SYSTEM. 

than  nine  days,  and  the  outer  in  thiiteen  days  aud  a  half. 
The  existence  of  these  two  satellites  was  well  authenticated 
by  his  observations,  and  they  have  been  frequently  observed 
in  recent  times.  They  can  be  seen  with  a  telescope  of  one- 
foot  aperture  or  upwards.  Afterwards  Hei-schel  made  a  very 
assiduous  search  for  other  satellites.  He  encountered  many 
diihculties,  not  only  from  the  extreme  faintness  of  the  objects, 
but  from  the  difficulty  of  deciding  whether  any  object  he 
might  see  was  a  satellite,  or  a  small  star  which  happened  to 
be  in  the  neighborhood.  He  at  length  announced  the  probable 
existence  of  four  additional  satellites,  the  orbit  of  one  being 
inside  of  those  of  the  two  certain  ones,  one  between  them,  and 
two  outside  them.  This  made  an  entire  number  of  six;  and 
though  tlie  evidence  adduced  by  Herschel  in  favor  of  the  ex- 
istence of  the  four  additional  ones  was  entirely  insufficient, 
and  their  existence  has  been  completely  disproved,  they  figure 
in  some  of  our  books  on  astronomy  to  this  day. 

For  half  a  centuiy  no  telescope  more  powerful  than  that  of 
Herschel  was  turned  upon  Uranus,  and  no  additional  light  was 
thrown  upon  the  question  of  the  existence  or  non-existence  of 
the  questionable  objects.  At  length,  about  1846,  Mr.  William 
Lassell,  of  England,  constructed  a  reflector  of  two  feet  aper- 
ture, of  which  we  have  already  spoken,  and  of  very  excellent 
definition,  which  in  optical  power  exceeded  any  of  the  older 
instruments.  "With  this  he  succeeded  in  discovering  two  new 
satellites  inside  the  orbits  of  the  two  brighter  ones,"^  but  found 
no  trace  of  any  of  the  additional  satellites  of  Hei-schel.  In  tlie 
climate  of  England,  he  could  make  only  very  imperfect  obser- 
vations of  these  bodies;  but  in  1852  lie  moved  his  telescope 
temporarily  to  Malta,  to  take  advantage  of  the  purer  sky  of 
that  latitude,  aud  there  he  succeeded  in  detennining  their  or- 
bits with  considerable  accuracy.  Their  times  of  revolution 
are  about  2^  and  4:  days  respectively.     They  may  fairly  be 

*  These  diflBcalt  objects  were  also  sought  for  by  Otto  Struve  with  the  fifteen- 
inch  telescope  of  the  Pulkowa  Obsenatory,  and  occasional  glimpses  of  them  were, 
he  believed,  attained  before  they  were  certainly  found  by  Mr.  Lassell.  but  he  wa| 
oot  able  to  follow  them  so  continaouslj  as  to  fix  upon  their  times  of  revolution. 


VBANUS  AND  ITS  SATELLITES.  365 

regarded  as  the  most  diflScult  known  objects  in  the  planetary 
system;  indeed,  it  is  only  with  a  few  of  the  most  powerful 
telescopes  in  existence  that  they  have  certainly  been  seen. 

The  non-existence  of  Herschel's  suspected  satellites  is  proved 
by  the  fact  that  they  have  been  sought  for  in  vain,  both  with 
Mr,  Lassell's  great  reflectors  and  with  the  Washington  twen- 
ty-six-inch refractor,  all  of  which  are  optically  more  powerful 
than  the  telescopes  of  Herschel.  There  may  be  additional 
satellites  which  have  not  yet  been  discovered  ;  but  if  so,  they 
must  be  too  faint  to  have  been  recognized  by  Herschel.  Pro- 
fessor Ilolden,  of  the  Naval  Observatory,  has  sought  to  show 
that  some  of  Herschel's  observations  of  his  supposed  inner  sat- 
ellites were  really  glimpses  of  the  objects  afterwards  discov- 
ered by  Mr.  Lassell.  This  he  has  done  by  calculating  the  po- 
sitions of  these  imier  satellites  from  tables  for  the  date  of 
each  of  Herschel's  observations,  and  comparing  them  with  the 
position  of  the  object  noted  by  Herschel.  In  four  cases,  the 
agreement  is  suflicientiy  close  to  warrant  the  belief  that  Her- 
schel actually  saw  the  real  satellites;  but  Mr.  Lassell  attributes 
tliese  coincidences  to  chance,  and  contests  Professor  Holden's 
views. 

The  most  remarkable  peculiarity  of  the  satellites  of  Uranus 
is  the  great  inclination  of  their  orbits  to  the  ecliptic.  Instead 
of  being  inclined  to  it  at  small  angles,  like  the  orbits  of  all 
the  other  planets  and  satellites,  they  are  nearly  perpendicular 
to  it;  indeed,  in  a  geometrical  sense,  they  are  more  than  per- 
pendicular, because  the  direction  of  the  motion  of  the  satel- 
lites in  their  orbits  is  retrograde.  To  change  the  position  of 
the  orbit  of  an  ordinary  satellite  into  that  of  the  orbits  of 
these  satellites,  it  would  have  to  be  tipped  over  100°  ;  so  that, 
supposing  the  orbit  a  horizontal  plane,  the  point  correspond' 
ing  to  the  zenith  would  be  10°  below  the  horizon,  and  the  up- 
per surface  would  be  inclined  beyond  the  perpendicular,  so  as 
to  be  the  lower  of  the  two  surfaces. 

Observations  of  the  satellites  afford  the  only  accurate  way 
of  determining  the  mass  of  Uranus  ;  because,  of  the  adjoining 
planets,  Saturn  and  Neptune,  the  observations  of  the  first  ara 


366  THE  SOLAR  SYSTEM. 

too  uncertain  and  those  of  the  last  too  recent  to  give  any  cen 
tain  result  Measures  made  with  the  great  Washington  tele* 
scope  show  this  mass  to  be  irjioTr  '■>  ^  result  which  is  probably 
correct  within  -^^  part  of  its  whole  amount.* 

§  8.  Neptune  and  its  Satellite. 

The  discovery  of  this  planet  is  due  to  one  of  the  boldest  and 
most  brilliant  conceptions  of  modern  astronomy.  The  planet 
was  felt,  as  it  were,  by  its  attraction  upon  Uranus;  and  its  di- 
rection was  thus  calculated  by  the  theory  of  gravitation  before 
it  had  been  recognized  by  the  telescope.  An  observer  was 
told  that  if  he  pointed  his  telescope  towards  a  certain  point  in 
the  heavens,  he  would  see  a  new  planet.  He  looked,  and  there 
was  the  planet,  within  a  degree  of  the  calculated  place.  It  is 
difficult  to  imagine  a  more  striking  illustration  of  the  certain- 
ty of  that  branch  of  astroi:omy  which  treats  of  the  motions  of 
the  heavenly  bodies  and  is  founded  on  the  theory  of  gravi- 
tation. 

To  describe  the  researches  which  led  to  this  result,  we  shall 
have  to  go  back  to  1820.  In  that  year,  Bouvard,  of  Paris, 
prepared  improved  tables  of  Jupiter,  Saturn,  and  Uranus, 
which,  althou'2;h  now  very  imperfect,  have  formed  the  basis  of 
most  of  the  calculations  since  made  on  the  motions  of  those 
bodies.  He  found  that  while  the  motions  of  Jupiter  and  Sat- 
urn were  fairly  in  accord  with  the  theory  of  gravitation,  it 
was  not  so  with  those  of  Uranus.  After  allowing  for  the  per- 
turbations produced  by  the  known  planets,  it  was  impossible 
to  iind  any  orbit  which  would  satisfy  both  the  ancient  and  the 
recent  observations  of  Uranus.  By  the  ancient  observations 
we  mean  those  accidental  nes  made  by  Flamsteed,  Le  Mon- 
nier,  and  others,  before  the  planetary  character  of  the  object 
was  suspected ;  and  by  the  recent  ones,  those  made  after  the 
discovery  of  the  planet  by  Herschel,  in  1781.  Bouvard,  there- 
fore, rejected  the  older  observations,  founding  his  tables  on  the 
modern  ones  alone ;  and  leaving  to  future  investigator  the 

*  Washington  Observations  for  1873:  Appendix. 


NEPTUNE  AND  ITS  SATELLITE.  367 

question  whether  the  difficulty  of  reconciling  the  two  systems 
arose  from  the  inaccuracy  of  the  ancient  observations,  or  from 
the  action  of  some  extraneous  influence  upon  the  planet. 

Only  a  few  years  elapsed,  when  the  planet  began  to  deviate 
from  the  tables  of  Bouvard.  In  1830  the  error  amounted  to 
80";  in  1S40,  to  90";  in  1844,  to  2'.  From  a  non-astro- 
uumical  point  of  view,  these  deviations  were  very  minute 
ilad  two  stars  moved  in  the  heavens,  the  one  in  the  place 
of  the  real  planet,  the  other  in  that  of  the  calculated  planet, 
it  would  have  been  an  eye  of  wonderful  keenness  which 
could  have  distinguished  the  two.  from  a  single  star,  even  in 
1844.  But,  magnified  by  the  telescope,  it  is  a  large  and 
easily  measurable  quantity,  not  for  a  moment  to  be  neglect- 
ed. The  probable  cause  of  the  deviation  was  sometimes  a 
subject  of  discussion  among  astronomers,  but  no  very  definite 
views  respecting  it  seem  to  have  been  entertained,  nor  did 
any  one  express  the  decided  opinion  that  it  was  to  be  attrib- 
uted to  a  trans-Uranian  planet,  natural  as  it  seems  to  us  such 
an  opinion  would  have  been. 

In  1845,  Arago  advised  his  then  vouno-  and  unknown  friend 
Leverrier,  whom  he  knew  to  be  an  able  mathematician  and 
an  expert  computer,  to  investigate  the  subject  of  the  motions 
of  Uranus.  Leverrier  at  once  set  about  the  task  in  the  most 
systematic  maimer.  The  first  step  was  to  make  sure  that  the 
deviations  did  not  arise  from  errors  in  Bouvard's  theory  and 
tables;  he  therefore  commenced  with  a  careful  recomputation 
of  the  perturbations  of  Uranus  produced  by  Jupiter  and  Sat- 
urn, and  a  critical  examination  of  the  tables.  The  result  was 
the  discovery  of  many  small  errors  in  the  tables,  wiiich,  how- 
ever, were  not  of  a  character  to  give  rise  to  the  observed  de- 
viations. 

The  next  question  was  whether  any  orbit  could  be  assigned 
which,  after  making  allowance  for  the  action  of  Jupiter  and 
Saturn,  would  represent  the  modern  observations.  The  an- 
swer was  in  the  negative,  the  best  orbit  deviating,  first  on  one 
side  and  then  on  the  other,  by  amounts  too  great  to  be  attrib- 
uted to  errors  of  observation.  Supposing  the  deviations  to  be 
a  25 


368  T^^  SOLAS  SYSTEM. 

due  to  the  attraction  of  some  unknown  planet,  Lcverrier  next 
inquired  where  this  planet  must  be  situated.  Its  orbit  could 
not  lie  between  those  of  Saturn  and  Uranus,  because  then  it 
would  disturb  the  motions  of  Saturn  as  well  as  those  of  Uranus. 
Outside  of  Uranus,  therefore,  the  planet  must  be  looked  for, 
and  probably  at  not  far  from  double  the  distance  of  that 
bodv ;  this  being:  the  distance  indicated  by  the  law  of  Titius. 
Complete  elements  of  the  orbit  of  the  unseen  planet  were 
finally  deduced,  making  its  longitude  325°  as  seen  from  the 
earth  at  the  beo-innino^  of  1847.  This  conclusion  was  reached 
in  the  summer  of  1846. 

Leverrier  was  not  alone  in  reaching  this  result.  In  1843, 
Mr.  John  C.  Adams,  then  a  student  at  Cambridge  University, 
England,  having  learned  of  the  discordances  in  the  theory  of 
Uranus  from  a  report  of  Professor  Airy,  attacked  the  same 
problem  which  Leverrier  took  hold  of  two  years  later.  In 
October,  1845,  he  communicated  to  Professor  Airy  elements 
of  the  planet  so  near  the  truth  that,  if  a  search  had  been  made 
with  a  large  telescope  in  the  direction  indicated,  the  planet 
could  hardly  have  failed  to  be  found.  The  Astronomer  Royal 
was,  however,  somewhat  incredulous,  and  deferred  his  search 
for  further  explanations  from  Mr.  Adams,  which,  from  some 
unexplained  cause,  he  did  not  receive.  Meanwhile  the  planet, 
which  had  been  in  opposition  about  the  middle  of  August, 
was  lost  in  the  rays  of  the  sun,  and  could  not  be  seen  before 
the  following  summer.  A  most  extraordinary  circumstance 
was  that  nothing  was  immediately  published  on  the  subject  of 
Mr.  Adams's  labors,  and  no  effort  made  to  secure  his  right  to 
priority,  although  in  reality  his  researches  preceded  those  of 
Leverrier  by  nearly  a  year. 

In  the  summer  of  1846,  M.  Leverrier's  elements  appeared, 
and  the  coincidence  of  his  results  with  those  of  Mr.  Adams 
was  so  striking,  that  Professor  Challis,  of  the  Cambridge  Ob- 
servatory, commenced  a  vigorous  search  for  the  planet.  Un- 
fortunately, he  adopted  a  mode  of  search  which,  although  it 
made  the  discovery  of  the  planet  certain,  was  extremely  la- 
borious.    Instead  of  endeavoring  to  recognize  it  by  its  disk, 


NEPTUNE  AND  ITS  SATELLITE.  369 

he  sought  to  detect  it  by  its  motion  among  the  stars  —  a 
course  which  required  all  the  stars  in  the  neighborhood  to 
have  their  positions  repeatedly  determined,  so  as  to  find 
which  of  them  had  changed  its  position.  Observations  of 
the  planet  as  a  star  were  actually  made  on  August  4:th,  1846, 
and  again  on  August  12th ;  bat  these  observations,  owing  to 
Mr.  Challis's  other  engagements,  were  not  reduced,  and  so  the 
fact  that  the  planet  was  observed  did  not  appear.  His  mode 
of  proceeding  was  much  like  that  of  a  man  who,  knowing  that 
a  diamond  had  dropped  near  a  certain  spot  on  the  sea-beach, 
should  remove  all  the  sand  in  the  neighborhood  to  a  conven- 
ient place  for  the  purpose  of  sifting  it  at  his  leisure,  and 
should  thus  have  the  diamond  actually  in  his  possession  w^ith- 
out  being  able  to  recognize  it. 

Early  in  September,  1846,  while  Professor  Challis  was  still 
working  away  at  his  observations,  entirely  unconscious  that 
the  great  object  of  search  was  securely  imprisoned  in  the  pen- 
cilled figures  of  his  note-book,  Leverrier  wrote  to  Dr.  Galle,  at 
Berlin,  suggesting  that  he  should  try  to  find  the  planet.  It 
happened  that  a  map  of  the  stars  in  the  region  occupied  by 
the  planet  was  just  completed,  and  on  pointing  the  telescope 
of  the  Berlin  Observatory,  Galle  soon  found  an  object  which 
had  a  planetary  disk,  and  was  not  on  the  star  map.  Its  posi- 
tion was  carefully  determined,  and  on  the  night  following  it 
was  re-examined,  and  found  to  have  changed  its  place  among 
the  stars,  No  farther  doubt  could  exist  that  the  loncr-sousrht- 
for  planet  was  found.  The  date  of  the  optical  discovery  was 
September  23d,  1846.  The  news  reached  Professor  Challis 
October  1st,  and,  looking  into  his  note-book,  he  found  his  own 
observations  of  the  planet,  made  nearly  two  months  before. 

As  between  Leverrier  and  Adams,  the  technical  right  of 
priority  in  this  wonderful  investigation  lay  with  Leverrier,  al- 
though Adams  had  preceded  him  by  nearly  a  year,  for  the 
double  reason  that  the  latter  did  not  publish  his  results  before 
the  discovery  of  the  planet,  and  that  it  was  by  the  directions 
of  Leverrier  to  Dr.  Galle  that  the  actual  discovery  was  made. 
But  this  does  not  diminish  the  credit  due  to  Mr.  Adams  foj 


370  THE  SOLAR  SYSTEM. 

his  boldness  in  attacking,  and  his  skill  in  successfully  solving, 
60  noble  a  problem.  The  spirit  of  true  science  is  advancing 
to  a  stage  in  which  contests  about  priority  are  looked  upon  as 
below  its  dignity.  Discoveries  are  made  for  the  benefit  of 
mankind ;  and  if  made  independently  by  several  persons,  it  is 
fitting  that  each  should  receive  all  the  credit  due  to  success  in 
making  it.  We  should  consider  Mr.  Adams  as  entitled  to  the 
same  unqualified  admiration  which  is  due  to  a  sole  discoverer; 
and  whatever  claims  to  priority  he  may  have  lost  by  the  more 
fortunate  Leverrier  will  be  compensated  by  the  sympathy 
which  mnst  ever  be  felt  towards  the  talented  young  student 
in  his  failure  to  secure  for  his  work  that  immediate  publicity 
which  was  due  to  its  interest  and  importance. 

The  discovery  of  Neptune  gave  rise  to  a  series  of  research- 
es, in  which  American  astronomers  took  a  distinguished  part. 
One  of  the  fii*st  questions  to  be  considered  was  whether  the 
planet  had, like  Uranus,  been  observed  as  a  star  by  some  pre- 
vious astronomer.  This  question  was  taken  np  by  Mr.  Sears  C. 
Walker,  of  the  Kaval  Observatory.  A  few  months'  observa- 
tion sufliced  to  show  that  the  distance  of  the  planet  from  the 
sun  was  not  far  from  30  (the  distance  of  the  earth  being,  as 
usual,  unity),  and,  assuming  a  circular  orbit,  he  computed  the 
approximate  place  of  the  planet  in  past  years.  He  traced  its 
course  back  from  year  to  year  in  order  to  find  whether  at  any 
time  it  passed  through  a  region  M'hicli  was  at  the  same  time 
being  swept  by  the  telescopes  of  observers  engaged  in  prepar- 
ing catalogues  of  stars.  He  was  not  successful  till  he  reached 
the  year  1795.  On  the  8th  and  10th  of  May  of  that  year, 
Lalande,  of  Paris,  had  swept  over  the  place  of  the  planet.  It 
must  now  be  decided  whether  any  of  the  stars  observed  on 
those  nights  could  have  been  Neptune.  Although  the  exact 
place  of  the  planet  could  not  yet  be  fixed  for  an  epoch  so 
remote,  it  was  easy  to  mark  out  the  apparent  position  of  its 
orbit  as  a  line  among  the  stars,  and  it  must  then  have  been 
somewhere  on  that  line.  After  taking  out  the  stars  which 
were  too  far  from  the  line,  and  those  which  had  been  seen  by 
subsequent  observers,  there  remained  one,  observed  on  Ma;y 


NEPTUNE  AND  ITS  SATELLITE.  371 

10th,  which  was  very  near  the  computed  orbit.  "Walker  at 
once  ventured  on  the  bold  prediction  that  if  this  region  of 
the  heavens  were  examined  with  a  telescope,  that  star  would 
be  found  missing.  He  communicated  this  opinion  officially 
to  Lieutenant  Maury  and  other  scientific  men  in  Washington, 
and  asked  that  the  search  might  be  made.  On  the  first  clear 
evening  the  examination  was  made  by  Professor  Hubbard, 
and,  surely  enough,  the  star  was  not  there. 

There  was,  however,  one  weak  point  in  the  conclusion  that 
this  was  really  the  planet  Neptnne.  Lalande  had  marked  hia 
observation  of  the  missing  star  with  a  colon,  to  indicate  that 
there  was  a  doubt  of  its  accuracy :  therefore  it  was  possible 
that  the  record  of  the  supposed  star  might  have  been  the  sim- 
ple result  of  some  error  of  observation.  Happily,  the  original 
manuscripts  of  Lalande  were  carefully  preserved  at  the  Paris 
Observatory ;  and  as  soon  as  the  news  of  Walker's  researches 
reached  that  city  an  examination  of  the  observations  of  May 
8th  and  10th,  1795,  was  entered  upon.  The  extraordinary  dis- 
covery was  made  that  there  was  no  mark  of  uncertainty  in  the 
original  record,  but  that  Lalande  had  observed  the  planet  both 
on  the  8tli  and  10th  of  May.  The  object  having  moved  slight- 
ly during  the  two  days'  interval,  tlie  observations  did  not 
agree  ;  and  Lalande  supposed  that  one  of  them  must  be  wrong, 
entirely  unconscious  that  in  that  little  discrepancy  lay  a  dis- 
covery which  would  have  made  his  name  immoi'tal.  Without 
further  examination,  he  had  rejected  the  first  observation,  and 
copied  the  second  as  doubtful  on  account  of  the  discrepancy, 
and  thus  the  pearl  of  great  price  was  dropped,  not  to  be 
found  again  till  a  half-century  had  elapsed. 

For  several  years  the  investigation  of  the  motion  of  the  new 
planet  was  left  in  the  hands  of  Mr.  Walker  and  Professor 
Peirce.  The  latter  was  the  first  one  to  compute  the  perturba^ 
tions  of  Neptune  produced  by  the  action  of  the  other  planets. 
The  results  of  these  computations,  together  with  Mr.  Walk- 
er's elements,  are  given  in  the  Proceedings  of  the  American 
Academy  of  Arts  and  Sciences. 

Physical  Aspect  of  Neptune. — On  the  physical  appearance  of 


372  THE  SOLAR  SYSTEM. 

this  planet  very  little  can  be  said.  In  the  largest  telescopea 
and  throngh  the  finest  atmosphere,  it  presents  the  appearance 
of  a  perfectly  round,  disk  about  3"  in  diameter,  of  a  pale-bine 
color.  Xo  markings  have  been  seen  upon  it.  When  first 
seen  by  Mr,  Lassell,  he  suspected  a  ring,  or  some  such  append- 
age ;  but  future  observations  under  more  favorable  circum- 
stances showed  this  suspicion  to  be  without  foundation.  To 
recognize  the  disk  of  Xeptune  with  ease,  a  magnifying  power 
of  300  or  upwards  must  be  employed. 

Satellite  of  Xeptune. — Soon  after  the  discovery  of  Xeptune, 
Mr.  Lassell,  scnitiuizing  it  with  his  two-foot  reflector,  saw  on 
various  occasions  a  point  of  light  in  the  neighborhood.  Dur- 
ing the  following  year  it  proved  to  be  a  satellite,  having  a  pe- 
riod of  revolution  of  about  5  days  21  hours.  During  1847 
and  1S4S  the  satellite  was  observed,  both  at  Cambridge  by  the 
Messrs.  Bond,  and  at  Pulkowa  by  Struve.  These  observations 
showed  that  its  orbit  was  inclined  about  30°  to  the  ecliptic, 
but  it  was  impossible  to  decide  in  which  direction  it  was  mov- 
ing, since  there  were  two  positions  of  the  orbit,  and  two  di- 
rections of  motion,  in  which  the  apparent  motion,  as  seen  from 
the  earth,  would  be  the  same.  After  a  few  years  the  change 
in  the  direction  of  the  planet  enabled  this  question  to  be  de- 
cided, and  showed  that  the  motion  was  retrograde.  The  case 
was  more  extraordinary  than  that  of  the  satellites  of  Uranus, 
Cince,  to  represent  both  the  position  of  the  orbit  and  the  di- 
rection of  motion  in  the  usual  way,  the  orbit  would  have  to  be 
tipped  over  150^  ;  it  is,  in  fact,  nearly  upside  down.  The  de- 
terminations of  the  elements  of  the  satellite  have  been  ex- 
tremely discordant,  a  circumstance  which  we  must  attribute 
to  its  extreme  faintness.  It  is  a  minute  object,  even  in  the 
most  powerful  telescopes. 

Measures  of  the  distance  of  the  satellite  from  the  planet, 
made  with  the  great  Washington  telescope,  show  the  mass  of 
Xeptune  to  be  xrrsTr-  The  mass  deduced  from  the  perturba- 
tions of  Uranus  is  TFTrnr?  ^^  agreement  as  good  as  could  ba 
expected  in  a  quantity  so  diflicult  to  determine. 


ASPECTS  AND  FOEMS  OF  COMETS.  373 


CHAPTER  V. 

COMETS    AND    METEORS. 

§  1.  Aspects  and  Forms  of  Comets. 

Tiis  celestial  motions  which  we  have  hitlierto  described 
take  place  with  a  majestic  uniformity  which  has  always  im- 
pressed the  minds  of  men  with  a  sense  of  the  unchangeable- 
ness  of  the  heavens.  But  this  uniformity  is  on  some  occasions 
broken  by  the  apparition  of  objects  of  an  extraordinary  as- 
pect, which  hover  in  the  heavens  for  a  few  days  or  weeks,  like 
some  supernatural  visitor,  and  then  disappear.  We  refer  to 
comets,  bodies  which  have  been  known  from  the  earliest  times, 
but  of  which  the  nature  is  not  yet  deprived  of  mysteiy. 

Comets  bright  enough  to  be  noticed  with  the  naked  eye 
consist  of  three  parts,  which,  howevei',  are  not  completely  dis- 
tinct, but  run  into  each  other  by  insensible  degrees.  These 
are  the  nucleus,  the  coma,  and  the  tail. 

The  nucleus  is  the  bright  centre  which  to  tlie  eye  presents 
the  appearance  of  an  ordinary  star  or  planet.  It  would  hard- 
ly excite  remark  but  for  the  coma  and  tail  by  which  it  is  ac- 
companied. 

The  coma  (which  is  Latin  for  hair)  is  a  mass  of  cloudy  or 
vaporous  appearance,  which  surrounds  the  nucleus  on  all  sides. 
Next  to  the  nucleus,  it  is  so  bi'ight  as  to  be  hardly  distinguish- 
able from  it,  but  it  gradually  shades  off  in  every  direction. 
Nucleus  and  coma  combined  present  the  appearance  of  a  star, 
more  or  less  bright,  shining  through  a  small  patch  of  fog,  and 
are  together  called  the  head  of  the  comet. 

The  tail  is  a  continuation  of  the  coma,  and  consists  of  a 
stream  of  milky  light,  growing  widei-  and  fainter  as  it  recedes 
from  the  comet,  until  the  eye  can  no  longer  trace  it.     A  curi' 


374:  THE  SOLAR  SYSTEM- 

ons  feature,  noticed  from  the  earliest  times,  is  that  the  tail  is 
alwavs  turned  from  tiie  sun.  The  extent  of  the  tail  is  very 
diiferent  in  different  comets,  that  appendage  being  brighter 
and  longer  the  more  brilliant  the  comet.  Sometimes  it  might 
almost  escape  notice,  while  in  many  great  comets  recorded  in 
history  it  has  extended  half-way  across  the  heavens.  The 
actnal  length,  when  one  is  seen  at  all,  is  nearly  always  many 
millions  of  miles.  Sometimes,  though  rarely,  the  tail  of  the 
comet  is  split  up  into  several  branches,  extending  out  in 
slightly  different  directions. 

Such  is  the  general  appearance  of  a  comet  visible  to  the 
naked  eye.  AVhen  the  hea\ens  were  carefully  swept  with  tel- 
escopes, it  was  found  that  comets  thus  visible  formed  but  a 
Bmall  fraction  of  the  whole  number.  If  a  diligent  search  is 
kept  up,  as  many  comets  are  sometimes  found  with  the  tele- 
scope in  a  single  year  as  would  be  seen  in  a  lifetime  with  the 
unaided  eye.  These  '•  telescopic  comets  "  do  not  always  pre- 
sent the  same  aspect  as  those  seen  with  the  naked  eye.  The 
coma,  or  foggy  light,  generally  seems  to  be  developed  at  the 
expense  of  the  nucleus  and  the  tail.  Sometimes  either  no 
nucleus  at  all  can  be  seen  with  the  telescope,  or  it  is  so  faint 
and  ill-defined  as  to  be  hardly  distinguishable.  In  the  cases 
of  such  comets,  it  is  generally  impossible  to  distinguish  the 
coma  from  the  tail,  the  latter  being  either  entirely  invisible, 
or  only  an  elongation  of  the  coma.  Many  well-known  comets 
consist  of  hardly  anything  but  a  patch  of  foggy  light  of  more 
or  less  irregular  form. 

Notwithstanding  these  great  apparent  differences  between 
the  large  comets  and  the  telescopic  ones,  yet,  when  we  close- 
ly watch  their  respective  modes  of  development,  we  find  them 
rail  to  belong  to  one  class.  The  differences  are  like  those  be- 
tween some  animals,  which,  to  the  ordinary  looker-on,  have 
nothing  in  common,  but  in  which  the  zoologist  sees  that  every 
part  of  the  one  has  its  counterpart  in  the  other — indeed,  the 
analogy  between  what  the  astronomer  sees  in  the  growth  of 
comets  and  the  zoologist  in  the  growth  of  animals  is  qjite 
worthy  of  remark.     As  a  general  rule,  all  comets  look  nearlji 


ASPECTS  AND  FORMS   OF  COMETS. 


875 


Fio.  90.— Views  of  Eucke's  comet  iu  1871,  by  Dr.  Vogel. 


alike  when  they  first  come  within  reach  of  tlie  telescope,  tha 
subsequent  diversities  arising  from  the  different  developments 
of  corresponding  parts.  The  first  appearance  is  that  of  a  lit- 
tle foggy  patch  without  any  tail,  and  very  often  without  any 
visible  nucleus.  Thus,  in  the  case  of  Donati's  comet  of  1858, 
one  of  the  most  splendid  on  record,  it  was  more  than  two 
months  after  the  first  discovery  before  there  was  any  appear 


376  THE  SOLAR  SYSTEM. 

ance  of  a  tail.  To  enable  the  reader  to  see  the  relation  of 
this  to  a  very  diffused  telescopic  comet,  we  present  a  telescopic 
view  of  the  head  of  this  great  comet  when  near  its  brightest, 
and  three  drawings  of  Encke's  comet,  made  by  Dr.  Vogel,  in 
November  and  December,  1871. 

"When  the  nucleus  of  a  telescopic  comet  begins  to  show  it- 
self it  is  commonly  on  the  side  farthest  from  the  sun.  Sev- 
eral little  brandies  will  then  be  seen  stretched  out  in  the  di- 
rection of  the  sun,  so  that  it  will  appear  as  if  the  comet  had 
a  small  fan-shaped  tail  directed  towards  the  sun,  instead  of 
from  it,  as  is  usual.  Thus,  in  the  pictures  of  Encke's  comet 
in  Figs.  1  and  2,  the  sun  is  towards  the  left,  and  we  see  what 


Fig.  91. — Head  of  Donati's  great  comet  of  1S58,  after  Bond. 

looks  like  three  little  tails,  the  middle  one  pointed  towards  the 
pun.  But  if  we  look  at  the  view  of  Donati's  comet.  Fig.  91, 
we  see  several  little  lines  branching  upwards  from  the  centre 
of  the  head,  and  it  is  to  these,  and  not  to  the  tail,  that  the  lit- 
tle tails  in  the  figures  of  Encke's  comet  correspond.  In  fact, 
the  general  rule  is  that  the  heads  of  comets  have  a  fan-shaped 
structure,  the  handle  of  the  fan  being  in  the  nucleus,  and  the 
middle  arm  pointing  towards  the  sun  ;  and  it  is  this  append- 
age which  fii-st  shows  itself. 

In  the  larger  comets,  this  fan  is  surrounded  by  one  or  more 


MOTIONS,  ORIGIN,  AND  NUMBER   OF  COMETS.  377 

semicircular  arches,  or  envelopes,  the  inner  one  forming  its 
curved  border;  but  this  arch  does  not  show  itself  in  very  faint 
comets.  The  true  tail  of  the  comet,  when  it  appears,  is  always 
directed  from  the  sun,  and  tlierefore  away  from  the  fan.  In 
Fig.  90,  No.  3,  a  very  faint  true  tail  will  be  seen  extending 
out  towards  the  lower  right-hand  corner  of  the  picture,  wliich 
was  opposite  to  the  direction  of  the  sun.  On  the  other  hand, 
tliough  the  branches  turned  towards  the  sun  have  disappeared, 
the  fan-like  form  can  still  be  traced  in  the  head.  In  Fi<r.  91, 
the  true  tail  is  turned  downwards :  owing  to  the  large  scale  of 
the  picture,  only  the  commencement  of  it  can  be  seen.  Tlie 
central  line  of  the  tail,  it  will  be  remarked,  is  comparatively 
dark.     This  is  very  generally  the  case  with  bright  comets. 

§  2.  Ilotions,  Origin,  and  Number  of  Comets. 

When  it  was  found  by  Kepler  that  all  the  planets  moved 
around  the  sun  in  conic  sections,  and  when  Newton  showed 
that  this  motion  was  the  necessary  result  of  the  gravitation  of 
the  planets  towards  the  sun,  the  question  naturally  arose  wheth- 
er comets  moved  according  to  the  same  law.  It  was  found  by 
Newton  that  the  comet  of  1680  actuall}'^  did  move  in  such  an 
orbit,  but  instead  of  being,  like  the  planetary  orbits,  nearly 
circular,  it  was  very  eccentric,  being  to  all  appearance  a  pa- 
rabola. 

A  parabola  being  one  of  the  orbits  which  gravitation  would 
cause  to  be  described,  it  was  thus  made  certain  that  comets 
gravitated  towards  the  sun,  like  planets.  It  was,  however,  im- 
possible to  say  whether  the  orbit  was  really  a  parabola  or  a 
very  elongated  ellipse.  The  reason  of  this  difiicnlty  is  that 
comets  are  visible  in  only  a  very  small  portion  of  their  orbits, 
quite  close  to  the  sun,  and  in  this  portion  the  forms  of  a  pa- 
rabola and  of  a  very  eccentric  ellipse  are  so  nearly  the  same, 
that  they  cannot  always  be  distinguished. 

There  is  this  very  important  difference  between  an  elliptical 
and  a  parabolic  orbit  —  that  the  former  is  closed  up,  and  a 
comet  moving  in  it  must  come  back  some  time,  whereas  the 
two  branches  of  the  latter  extend  out  into  infinite  space  with- 


378 


THE  SOLAR  SYSTE.V. 


out  ever  meeting.  A  comet  moving  in  a  parabolic  orbit  will, 
therefore,  never  return,  but,  after  once  sweeping  past  the  sun, 
will  continue  to  recede  into  infinite  space  forever.  The  same 
thing  will  happen  if  the  comet  moves  in  an  hyperbola,  which  ia 


\  \ 


Paracolic  orbit.  Eccentric  ellipse. 

Pig.  92.— Parabolic  and  elliptic  orbit  of  a  comet.  The  comet  is  invisible  in  the  dotted  part 
of  the  orbits,  and  the  forms  of  the  visible  parts,  a,  b,  cannot  be  distinguished  in  the 
two  orbits.  But  the  e'-lipse  forms  a  closed  curve,  while  the  two  branches  of  the  pa- 
rabola continue  forever  witLont  meeting. 

the  tliird  class  of  orbit  that  may  be  described  under  the  influ- 
ence of  gravitatitn.  In  a  parabola,  tlie  slightest  retardation 
of  a  comet  would  change  the  orbit  into  an  ellipse,  the  velocity 
being  barely  sufficient  to  carry  the  comet  off  forever,  whereas 
in  an  hyperbola  there  is  more  or  less  velocity  to  spare.  Thus 
the  parabola  is  a  sort  of  dividing  curve  between  the  hyperbola 
and  the  ellipse. 

The  astronomer,  knowing  the  position  of  an  orbit,  can  tell 
exactly  what  velocity  is  necessary  at  any  point  of  it  in  order 
that  a  body  moving  in  it  may  go  off,  never  to  return.  A  body 
thrown  from  the  earth's  surface  %dth  a  velocity  of  seven  miiea 


MOTIONS,  ORIGIN,  AND  NUMBER   OF  COMETS.         379 

Q  second,  and  not  retarded  by  the  atmosphere,  would  never 
return  to  the  earth,  but  would  describe  some  sort  of  an  orbit 
round  the  sun.  It  would,  in  fact,  be  a  little  planet.  If  the 
earth  were  out  of  the  way,  a  body  moving  past  the  earth's 
orbit  at  the  rate  of  twenty-six  miles  a  second  would  have  just 
the  velocity  necessary  to  describe  a  parabola.  If  the  velocity 
of  a  comet  exceeds  this  limit  at  that  point  of  its  orbit  which 
is  92^  millions  of  miles  from  the  sun,  then  the  comet  must 
go  off  into  intinite  space,  never  to  return  to  our  system.  But 
with  a  less  velocity  the  comet  must  be  brought  back  by  the 
sun's  attraction  at  some  future  time,  the  time  being  longer  the 
more  i:iearly  the  velocity  reaches  twenty-six  miles  per  second. 
It  is  by  the  velocity  that  the  astronomer  must,  in  general,  de- 
termine the  form  of  the  orbit.  If  it  corresponds  exactly  to 
the  calculated  limit,  the  orbit  is  a  parabola ;  if  it  exceeds  this 
limit,  it  is  an  hyperbola  ;  if  it  falls  short  of  it,  it  is  an  ellipse. 

Now,  in  the  large  majority  of  comets  the  velocity  is  so  near 
the  parabolic  limit  that  it  is  not  possible  to  decide,  from  ob- 
servations, whether  it  falls  short  of  it  or  exceeds  it.  In  tho 
case  of  a  few  comets  the  observations  indicate  an  excess  of 
velocity,  but  the  excess  is  so  minute  that  its  reality  cannot  be 
confidently  asserted.  It  cannot,  therefore,  be  said  with  cer- 
tainty that  any  known  comet  revolves  in  a  hyperbolic  orbit,, 
and  thus  it  is  possible  that  all  comets  belong  to  our  system* 
and  will  ultimately  retui-n  to  it.  It  is,  however,  certain  that 
in  the  majority  of  cases  the  return  will  be  delayed  many  cen- 
turies, nay,  perhaps  many  thousand  years.  There  are  quite  a 
number  of  comets  which  are  known  to  be  periodic,  returning 
to  the  sun  at  regular  intervals  in  elliptic  orbits.  Some  of 
these  have  been  observed  at  several  returns,  so  that  their  exact 
period  has  been  determined  with  great  certainty :  in  the  case 
of  others,  the  periodicity  has  been  inferred  only  from  the  fact 
that  the  velocity  fell  so  far  short  of  the  parabolic  limit  that, 
there  could  be  no  doubt  of  the  fact  that  the  comet  moved  in 
an  ellipse. 

In  this  question  of  cometary  orbits  is  involved  the  very  in- 
teresting one,  whether  comets  should  be  considered  as  belong- 


380  THE  SOLAR  SYSTEM. 

ing  to  our  system,  or  as  mere  visitors  from  the  stellar  spaces. 
We  may  conceive  of  them  as  stray  fragments  of  original  neb- 
ulous matter  scattered  tlirough  the  great  %vilderness  of  space 
around  us,  drawn  towards  our  sun  one  by  one  as  the  long  ages 
elapse.  If  no  planets  surrounded  the  sun,  or  if,  surrounding 
it,  they  were  immovable,  a  comet  thus  drawn  in  would  whirl 
around  the  sun  in  a  nearly  parabolic  orbit,  and  leave  it  again, 
not  to  return  for  perhaps  millions  of  years,  because  the  veloci- 
ty it  would  acquire  by  falling  towards  the  sun  would  be  just 
sufficient  to  carry  it  back  into  the  infinite  void  from  which  it 
came.  But  owing  to  the  motions  of  the  several  planets  in 
their  orbits,  the  comet  would  have  its  velocity  changed  in 
passing  each  of  them,  the  change  being  an  acceleration  or  a 
retardation,  according  to  the  way  in  which  it  passed.  If  the 
total  accelerations  produced  by  all  the  planets  exceeded  the 
retardations,  the  comet  would  leave  our  system  with  more 
than  the  parabolic  velocity,  and  would  certainly  never  return. 
If  the  retarding  forces  chanced  to  be  in  excess,  the  orbit 
would  be  changed  into  an  ellipse  more  or  less  elongated,  ac- 
cording to  the  amount  of  this  excess.  In  the  large  majority 
of  cases,  the  retardation  would  be  so  slight  that  the  most  del- 
icate observations  could  not  show  it,  and  it  could  be  known 
only  by  calculation,  or  by  the  return  of  the  comet  after  tens 
or  hundreds  of  thousands  of  years.  But  should  the  comet 
chance  to  pass  very  near  a  planet,  especially  a  large  planet 
like  Jupiter,  the  retardation  might  be  so  great  as  to  make  the 
comet  revolve  in  an  orbit  of  quite  short  period,  and  thus  be- 
some  a  seemingly  permanent  member  of  our  system.  So  near 
an  approach  of  a  comet  to  a  planet  would  not  be  likely  to  oc- 
cur more  than  once  in  a  number  of  centuries,  but  every  timo 
it  lid  occur  there  would  be  an  even  chance  for  an  additional 
comet  of  short  period,  the  orbit  of  which  would,  at  first,  al- 
most intersect  that  of  the  planet  which  had  deranged  it.  It 
might  not,  however,  be  a  known  comet,  because  the  orbit 
might  be  wholly  beyond  the  reach  of  cur  vision. 

All  the   facts   connected  with   periodic   comets   tend  to 
strengthen  the  view  that  they  become  members  of  our  system 


MOTIONS,  ORIGIN,  AND  NUMBER   OF  COMETS.  381 

in  this  way.  The  majority  of  those  of  short  period  have  been 
entrapped  by  Jupiter.  Those  orbits  which  do  not  pass  near 
Jupiter  generally  pass  near  to  some  other  planet,  to  whose 
action  the  introduction  of  the  comet  is  probably  due.  The 
o;radnal  fading  away  of  most  of  the  comets  of  short  period, 
which  we  shall  describe  more  fully  hereafter,  gives  additional 
color  to  this  view. 

Number  of  Comets. — It  was  the  opinion  of  Kepler  that  the 
celestial  spaces  were  as  full  of  comets  as  the  sea  of  fish,  only 
a  small  proportion  of  them  coming  within  the  range  of  our 
telescopes.  That  only  an  insignificant  fraction  of  all  existing 
comets  have  ever  been  observed,  we  may  regard  as  certain. 
Owing  to  their  extremely  elongated  orbits,  they  can  be  seen 
only  when  near  their  perihelion,  and  as  it  is  probable  that  the 
period  of  revolution  of  the  large  majority  of  those  which  have 
been  observed  is  counted  by  thousands  of  years — if,  indeed, 
they  ever  return  at  all — our  observations  must  be  continued 
for  many  thousand  years  before  we  have  seen  all  which  come 
within  range  of  our  telescopes.  It  is  also  probable  that  all 
which  can  ever  be  seen  will  be  but  a  small  fraction  of  the 
number  which  exist,  because  a  comet  can  seldom  be  seen  un- 
less its  perihelion  is  cither  inside  tlie  orbit  of  the  earth,  or  but 
little  outside  of  it.  There  are  a  few  exceptions  to  the  rule 
that  only  such  comets  are  seen,  the  most  notable  one  being 
that  of  the  comet  of  1729,  which,  at  perihelion,  was  more  than 
four  times  the  earth's  distance  from  the  sun.  This  comet  must 
have  been  one  of  extraordinary  magnitude,  as  almost  every 
other  known  comet  would  have  disappeared  entirely  from  the 
most  powerful  telescopes  of  that  time,  if  placed  at  the  dis- 
tance at  which  it  was  observed. 

The  actual  number  of  comets  recorded  as  visible  to  the 
naked  eye  since  the  Christian  era  is  given  in  the  table  on  the 
following  page.* 

*  This  table  is  taken  at  second-hand,  principally  from  Arago  ("Astronomie 
Populaire,"  livre  xvii.,  chap.  xv.).  Arago  mentions  but  eight  as  visible  during 
the  eighteenth  century.  1  have  considered  the  number  ihiitj'-six,  given  by  Klein, 
ns  more  probable. 


382 


THE  SOLAR   SYSTEM. 


Years  of 

our  Era. 

N  Qinbvr 
of  ComeU. 

From      0  to 

100 

92 

"     101  " 

2<X) 

23 

"    201  " 

300 

44 

"    301  " 

400 

27 

"    401  " 

oOO 

IG 

*'    501   " 

GOO 

25 

"    fiOl  " 

700 

22 

"    701  " 

800 

16 

"    801   " 

900 

42 

'•    901  " 

1000 

26 

Years  of  our  Era, 


From  1001  to  llOO. 


1101 
1201 
1301 
1401 
1501 
1601 
1701 
1801 


1200. 
1300. 
1400. 
1.500. 
1600. 
1700. 
1800. 
1875. 


Number 
of  Comets. 


36 
26 
26 
29 
27 
31 
12 
36 
16 


111  round  numbers,  about  five  hundred  comets  visible  to  the 
naked  eye  have  been  recorded  since  our  era,  making  a  general 
average  of  one  every  four  years.  Besides  these,  nearly  two 
hundred  telescopic  comets  have  been  observed  since  the  in- 
vention of  the  telescope  ;  so  that  the  total  number  of  these 
bodies  observed  during  the  period  in  question  does  not  fall 
far  short  of  seven  hundred.  Several  new  telescopic  comets 
are  now  discovered  nearly  every  year,  the  number  sometimes 
ranging  up  to  six  or  eight.  It  is  probable  that  the  annual 
number  of  this  class  discovered  depends  very  largely  on  the 
skill,  assiduity,  and  good  -  fortune  of  the  astronomers  who 
chance  to  be  engaged  in  searching  for  them. 

§  3,  Remarkable  Comets. 

In  unenlightened  ages  comets  wei*e  looked  on  with  terror, 
as  portending  pestilence,  war,  the  death  of  kings,  or  other 
calamitous  or  remarkable  events.  Hence  it  happens  that  in 
the  earlier  descriptions  of  these  bodies,  they  are  genei-ally 
associated  with  some  contemporaneous  event.  The  descrip- 
tions of  tlie  comets  themselves  are,  however,  so  vague  and 
indefinite  as  to  l)e  entirely  devoid  of  either  instruction  or  in- 
terest, as  it  often  happens  that  not  even  their  course  in  the 
heavens  is  stated. 

Tiie  great  comet  of  1680  is,  as  already  said,  remarkable  for 
being  not  only  a  brilliant  comet,  but  the  one  by  which  Kew- 
ton  proved  that  comets  move  under  the  influence  of  the  gravi- 
tation of  the  sun.  It  fii*st  appeared  in  the  autumn  of  1680, 
and  continued  visible  most  of  the  time  till  the  following  spring. 


BEMABKABLE   COMETS.  383 

It  fell  down  almost  in  a  direct  line  to  the  sun,  passing  nearer 
to  that  luminary  than  any  comet  before  known.  It  passed  its 
perihelion  on  December  18th,  and,  sweeping  round  a  large 
arc,  went  back  in  a  direction  not  very  different  from  that  from 
which  it  came.  The  observations  have  been  calculated  and 
the  orbit  investigated  by  many  astronomers,  beginning  witii 
Newton ;  but  the  results  show  no  certain  deviation  from  a 
parabolic  orbit.  Hence,  if  the  comet  ever  returns,  it  is  only 
at  very  long  intervals.  Halley,  however,  suspected,  with  some 
plausibility,  that  the  period  might  be  575  years,  from  the  fact 
that  great  comets  had  been  recorded  as  appearing  at  that  in- 
terval. The  first  of  these  appearances  was  in  the  month  of 
September,  after  Julius  Caesar  was  killed ;  the  second,  in  the 
year  531 ;  the  third,  in  Febriiarj^,  1106 ;  while  that  of  1680 
made  the  fourth.  If,  as  seems  not  impossible,  these  were  four 
returns  of  one  and  the  same  comet,  a  fifth  return  will  be  seen 
by  our  posterity  about  the  year  2255.  Until  that  time  the 
exact  period  must  remain  doubtful,  because  observations  made 
two  centuries  ago  do  not  possess  the  exactitude  wliicli  will 
decide  so  delicate  a  point. 

Halley  s  Comet — Two  years  after  the  comet  last  described, 
one  appeared  which  has  since  become  the  most  celebrated  of 
modern  times.  It  was  first  seen  on  August  19th,  1682,  and 
observed  about  a  month,  when  it  disappeared.  Halley  com- 
puted the  position  of  the  orbit,  and,  comparing  it  with  previ- 
ous orbits,  found  that  it  coincided  so  exactly  with  that  of  a 
comet  observed  by  Kepler  in  1607,  that  there  could  be  no 
doubt  of  the  identity  of  the  two  orbits.  So  close  were  they 
together  that,  if  drawn  on  the  heavens,  the  naked  eye  would 
almost  see  them  joined  into  a  single  line.  The  chances  against 
two  separate  comets  moving  in  the  same  orbit  were  so  great 
that  Halley  could  not  doubt  that  the  comet  of  1682  was  the 
same  that  had  appeared  in  1607,  and  that  it  therefore  revolved 
in  a  very  elliptic  orbit,  returning  about  every  seventy-five  years. 
His  conclusion  was  confirmed  by  the  fact  that  a  comet  was 
observed  in  1531,  which  moved  in  apparently  the  same  orbit. 
Again  subtracting  the  period  of  seventy -five  years,  it  was 

26 


384  THE  SOLAR  SYSTEM. 

found  that  the  comet  had  appeared  in  1456,  when  it  sprend 
6iich  terror  throughout  Christendom  that  Pope  Calixtus  or- 
dered prayers  to  be  offered  for  protection  against  the  Turks 
and  the  comet.  This  is  supposed  to  be  the  circumstance  which 
gave  rise  to  the  popular  mvth  of  tlie  Pope's  Bull  against  the 
Comet.  , 

This  is  the  earliest  occasion  on  which  observations  of  the! 
coui'se  of  the  comet  were  made  with  such  accuracy  that  its 
orbit  could  be  determined.  If  we  keep  subti-actiiig  7o|  years, 
we  sliall  find  that  we  sometimes  fall  on  dates  when  the  appa- 
rition of  a  comet  was  recorded ;  but  without  any  knowledge 
of  the  orbits  of  these  bodies,  it  cannot  be  said  with  certainty 
that  they  are  identical.  However,  in  the  returns  of  1456, 
1531,  1607,  and  1682,  at  nearly  equal  intervals,  Halley  had 
good  reason  for  predicting  that  the  comet  would  return  again 
about  175S.  This  gave  the  mathematicians  time  to  investi- 
gate its  motions ;  and  the  establishment,  in  the  mean  time,  of 
the  theory  of  gravitation  showed  them  how  to  set  about  the 
work.  It  was  necessary  to  calculate  the  effect  of  the  attrac- 
tion of  the  planets  on  the  motion  of  the  comet  during  the  en- 
tire seventy-six  years.  This  immense  labor  was  performed  by 
Clairaut,  who  found  that,  in  consequence  of  the  attractions  of 
Jupiter  and  Saturn,  the  return  of  the  comet  would  be  delayed 
618  days,  so  that  it  would  not  reach  its  perihelion  until  the 
middle  of  April,  1759,  Not  having  time  to  finish  his  calcula- 
tions in  the  best  way,  he  considered  that  tliis  result  was  nncer 
tain  by  one  month.  The  comet  actually  did  pass  its  perihelion 
at  midnight  on  March  12th,  1759. 

Seventy-six  years  more  were  to  elapse,  and  the  comet  would 
again  appear  about  1835.  Meanwliile,  great  improvements 
were  made  in  the  methods  of  computing  the  effects  of  planet- 
ary attraction  on  the  motions  of  a  comet,  so  that  mathemati- 
cians, without  expending  more  labor  tlian  Clairaut  did,  were 
enabled  to  obtain  much  more  accurate  results.  The  computa- 
tion of  the  return  of  the  comet  was  undertaken  independently 
by  four  leading  astronomers,  De  Damoiseau  and  De  Pontecou- 
lan'-  of  France,  and  Rosenberger  and  Lehmann  of  Germany. 


REMARKABLE  COMETS. 


385 


Professor  Rosenberger  announced  that  it  would  reach  its  peri- 
helion on  November  11th,  1835;  while  De  rontecoulant,  after 
revising  his  computations  with  more  exact  determinations  of 
the  masses  of  the  planets,  assigned  November  13th,  at  2  a.m.. 
as  the  date.  The  expected  comet  was  first  seen  on  August  5t]i. 
Approaching  the  suri,  it  passed  its  perihelion  on  Novemhei* 
16th,  only  three  days  after  the  time  predicted  by  De  Pontt- 
coulant,  and  five  days  after  that  of  Rosenberger.  But  althoiigli 
De  Pontecoulant's  result  was  nearest,  this  was  an  accident; 
the  work  of  Rosenberger  was  the  most  thorough. 

This  was  the  last  return  of  the  celebrated  comet  of  Ilalley. 
It  was  followed  until  May  17th,  1836,  when  it  disappeared 
from  the  sight  of  the  most  powerful  telescopes  of  the  time, 
and  has  not  been  seen  since.  But  tlie  astronomer  can  follow 
it  with  the  ej'e  of  science  witli  almost  as  much  certainty  as  if 
he  had  it  in  the  field  of  view  of  liis  telescope.  AVe  cannot  yet 
fix  the  time  of  its  return  with  certainty ;  but  we  know  that  it 
reached  the  farthest  limit 
of  its  course,  which  ex- 
tends some  distance  be- 
yond the  orbit  of  Nep- 
tune, about  1873,  and 
that  it  is  now  on  its  re- 
turn journey.  We  pre- 
sent a  diagram  of  its  or- 
bit, showing  its  position 
in  1874.  Its  velocity 
will  constantly  increase 
from  year  to  year,  and 

we      may      expect      it     to  Fm.  OS.-Oibit  of  Halley-s  comet. 

reach  perihelion  about  the  year  1911.  The  exact  date  caimot 
be  fixed  until  tlie  effect  of  the  action  of  all  the  planets  is  com- 
puted, and  this  will  be  a  greater  labor  than  before,  not  only 
because  greater  accuracy  will  be  aimed  at,  but  because  the 
action  of  more  planets  must  be  taken  into  account.  When 
Clairaut  computed  the  return  of  1759,  Saturn  was  the  outer- 
most known  planet.    When  the  return  of  1835  was  computed, 


386  TEE  SOLAR  SYSTEM. 

Uranus  had  been  added  to  the  list,  and  its  action  had  to  be 
taken  into  account.  Since  that  time  Xeptune  has  been  dis- 
covered; and  the  astronomer  who  computes  the  return  of  1911 
mnst  add  its  action  to  that  of  the  other  pLanets.  Bv  doing  so, 
we  niaj  liope  that  the  time  of  reaching  perihelion  will  be  pre- 
dicted within  one  or  two  days. 

The  Lost  Bielas  Comet. — Nothing  could  more  strikingly  il- 
lustrate the  difference  between  comets  and  other  heavenly 
bodies  than  the  fact  of  the  total  dissolution  of  one  of  the  for- 
mer. In  1S26,  a  comet  was  discovered  by  an  Austrian  named 
Biela,  which  was  found  to  be  periodic,  and  to  have  been  ob- 
served in  1772,  and  again  in  1805.  The  time  of  revolution 
was  found  to  be  six  years  and  eight  months.  In  the  next  two 
returns,  the  earth  was  not  in  the  riglit  part  of  its  orbit  to  ad- 
mit of  observing  the  comet ;  the  latter  was  therefore  not  seen 
again  till  1845.  In  November  and  December  of  that  year 
it  was  observed  as  usual,  without  anvthinoc  remarkable  beino: 
noticed.  But  in  January  following,  the  astronomers  of  the 
Naval  Observatoiy  found  it  to  have  suffered  an  accident  nev- 
er before  known  to  happen  to  a  heavenly  body,  and  of  which 
no  explanation  has  ever  been  given.  The  comet  had  sepa- 
rated into  two  distinct  parts,  of  quite  unequal  brightness,  so 
that  there  were  two  apparently  complete  comets,  instead  of 
one.  During  the  month  following,  the  lesser  of  the  two  con- 
tinually increased,  until  it  became  equal  to  its  companion. 
Then  it  grew  smaller,  and  in  March  vanished  entirely,  tliough 
its  companion  was  still  plainly  seen  for  a  month  longer.  The 
distance  apart  of  the  two  portions,  according  to  the  computa- 
tions of  Professor  Hubbard,  was  about  200,000  miles. 

The  next  return  of  the  comet  took  place  in  1852,  and  was, 
of  course,  looked  for  with  great  interest.  It  was  found  still 
divided,  and  the  two  parts  were  far  more  widely  separated 
than  in  1846,  their  distance  having  increased  to  about  a  mill- 
ion and  a  half  of  miles.  Sometimes  one  part  was  the  bright- 
er, and  sometimes  the  other,  so  that  it  was  impossible  to  de- 
cide which  ought  to  be  regarded  as  representing  the  principal 
comet.     The  pair  passed  out  of  view  about  the  end  of  Sep* 


REMARKABLE  COMETS.  387 

tember,  1852,  and  have  not  been  seen  since.  They  would, 
since  then,  have  made  five  complete  revolntions,  returning  in 
1859,  1865,  and  1872.  At  the  first  of  these  returns,  the  rela- 
tive positions  of  the  comet  and  the  earth  were  so  unfavorable 
that  there  was  no  hope  of  seeing  tlie  former.  In  1865,  it 
could  not  be  found ;  but  it  was  thought  tliat  this  might  be  due 
to  the  great  distance  of  the  comet  from  us.  In  1872,  the  rela- 
tive positions  were  extremely  favorable,  yet  not  a  trace  of  tlie 
object  could  be  seen.*  It  had  seemingly  vanished,  not  into 
thin  air,  but  into  something  of  a  tenuity  compared  with  which 
the  thinnest  air  was  as  a  solid  millstone.  Some  invisible  frag- 
ments were,  however,  passing  along  the  comet's  orbit,  and  pro- 
duced a  small  meteoric  shower,  as  will  be  explaiuL-d  in  a  later 
section.     Not  a  trace  of  the  comet  was  ever  again  seen. 

The  Great  Comet  o/ 1843. — This  remarkMble  comer  hurst 
suddenly  into  view  in  the  neighborhood  of  the  sun  about  the 
end  of  February,  IS-IS.  It  was  visible  in  full  daylight,  so  that 
some  observers  actually  measured  the  angular  distance  be- 
tween the  comet  and  the  sun.  It  was  followed  until  the  mid- 
dle of  April.  The  most  remarkable  feature  of  the  orbit  of 
this  comet  has  been  already  mentioned :  it  passed  nearer  the 
sun  than  any  other  known  body  —  so  near  it,  in  fact,  that, 
with  a  very  slight  change  in  the  dii-ection  of  its  original  mo- 
tion, it  would  actually  have  struck  it.  Its  orbit  did  not  cer- 
tainly deviate  from  a  parabola.  The  most  careful  investigation 
of  it — that  of  Professor  Hubbard,  of  Washington — indicated 
a  period  of  530  years  ;  but  the  velocity  which  would  produce 
this  period  is  so  near  the  parabolic  limit  that  the  difference 
does  not  exceed  the  uncertainty  of  the  observations. 

DonatVs  Comet  of  1858. — This  great  comet,  one  of  the  most 
magnificent  of  modern  times,  which  hung  in  the  western  sk}"! 
during  the  autumn  of  1858,  will  be  well  remembered  by  all 
who  were  then  old  enousrh  to  notice  it.     It  was  first  seen  at 


*  Just  after  the  meteoric  shower,  Mr.  Pogson,  of  Madras,  obtained  observa- 
tions of  an  object  which,  it  was  supposed,  might  have  been  a  fragment  of  this 
comet.  But  the  object  was  some  two  mouths  behind  the  computed  position  of 
the  comet,  so  that  the  identity  of  the  two  has  never  been  accepted  by  astronomers. 


3S8  THE  SOLAR  SYSTEM. 

Florence,  on  June  2d,  185S,  by  Donati,  who  described  it  as  a 
very  faint  nebulosity,  about  3'  in  diameter.  About  the  end 
of  the  month  it  was  discovered  independently  by  three  Amer- 
ican observei-s :  H.  P.  Tuttle,  at  Cambridge  ;  H,  M.  Parkhurst, 
at  Perth  Amboy,  New  Jereey  ;  and  Miss  Maria  Mitchel,  at 
Nantucket,  During  the  tii-st  three  months  of  its  visibility  it 
crave  no  indications  of  its  future  srrandeur.  Xo  tail  was  no- 
ticed  until  the  middle  of  August,  and  at  the  end  of  that 
month  it  was  only  half  a  degree  in  length,  while  the  comet 
itself  was  barely  visible  to  the  naked  eye.  It  continued  to 
approach  the  sun  till  the  end  of  September,  and  during  this 


Fig.  94. — Great  comet  of  ISSS. 


month  developed  with  great  rapidity,  attaining  its  greatest 
brilliancy  about  the  first  half  of  October.  Its  tail  was  then 
40°  in  length,  and  10°  in  breadth  at  its  outer  end,  and  of  a 
curious  feather-like  form.  About  October  20th  it  passed  so 
far  south  as  to  be  no  longer  visible  in  northern  latitudes ;  but 
it  was  followed  in  the  southern  hemisphere  until  March  fol- 
lowing. 

Observations  of  the  position  of  this  comet  soon  showed  its 
orbit  to  be  decidedly  elliptic,  with  a  period  of  about  2000 
years  or  less.  A  careful  iiivestigation  of  all  the  observations 
was  made  by  Mr.  G.  "W.  Hill,  who  found  a  period  of  1950 


THE  GREAT  SOUTHERN  COMET  OF  1880.  389 

years.  If  this  period  is  correct,  the  comet  must  have  appeared 
about  ninety-two  years  before  our  era,  and  must  appear  again 
about  the  year  3808  ;  but  the  uncertainty  arising  from  the  im- 
perfections of  the  observations  may  amount  to  fifty  years. 

The  Great  Southern  Comet  of  1880. — On  the  evening  of 
February  2d,  1880,  astronomers  in  South  America,  the  Cape 
of  Good  Hope,  and  Australia  were  surprised  to  see  wliat  was 
evidently  the  tail  of  a  huge  comet  rising  above  the  horizon 
in  the  south-west.  Its  length  was  40°,  Detailed  observations 
were  made  by  Dr.  Gould,  wlio  observed  it  at  Cordoba,  in  the 
Argentine  Republic.  It  was  not  until  two  days  afterwards, 
February  4th,  that  he  finally  saw  the  head  of  the  comet  through 
the  large  telescope.  It  w'as  then  moving  in  a  northerly  direc- 
tion, and,  it  was  supposed,  would  soon  pass  the  sun  and  be  visi- 
ble in  the  northern  hemisphere.  But,  instead  of  continuing  its 
northern  coui-se,  it  moved  rapidly  around  the  sun,  and  bent  its 
course  once  more  towards  the  south.  In  consequence,  it  did 
not  become  visible  in  tlie  northern  hemisphere  at  all. 

Tliis  rapid  motion  around  the  sun  showed  that  the  comet 
must  have  passed  very  near  that  object,  thus  reminding  astron- 
omers of  the  great  comet  of  1843.  When  the  elements  of  the 
orbit  were  computed  it  was  found  that  the  two  bodies  moved 
in  almost  the  same  orbit,  so  that  it  seemed  scarcely  possible 
to  avoid  the  conclusion  that  this  comet  was  a  return  of  the 
former  one.  Notwithstanding  the  seeming  evidence  in  favor 
of  this  view,  there  are  several  difficulties  in  the  way  of  its  un- 
reserved acceptance.  In  the  first  place,  the  most  careful  com- 
putations on  the  comet  of  1843  showed  no  deviation  from  a 
parabolic  orbit.  In  the  next  place,  if  this  was  a  retui-n  of  the 
former  comet,  it  should  have  appeared  at  regular  intervals 
of  thirty-six  years  and  eleven  months  in  former  times.  Now, 
there  is  no  record  of  such  a  comet  having  been  seen  at  the 
times  when  its  return  to  periiielion  should  have  occurred.  It 
is  true,  as  Dr.  Gould  showed,  that,  by  supposing  a  continuous 
change  in  the  period,  certain  comets  which  were  in  perihelion 
in  1688  and  1702  might  have  been  identical  with  tlie  two  in 
question.      This  would  have   required  the  period  to  change 


390  THE  SOLAR  SYSTEM. 

from  thirty-four  years  between  tlie  first  two  returns  to  tliirty- 
six  years  and  eleven  months  between  the  last  two.  Such  a 
change  is  so  improbable  tliat  we  can  hardly  regard  the  dif- 
ferent appearances  as  belonging  to  absolutely  the  same  bodies. 
The  most  probable  explanation  seems  to  be  that  they  were 
originally  two  nebulous  masses  far  out  in  the  stellar  spaces, 
and  that  the  nearer  one  was  drawn  into  the  sun  thirty-seven 
years  in  advance  of  the  more  distant  one. 

Great  Comet  0/ 1881. — This  comet  is  so  recent  that  most 
readers  will  remember  it.  It  was  first  heard  of  in  our  hemi- 
sphere through  a  telegram  from  Dr.  Gould,  stating  that  the 
comet  of  1807  was  in  five  hours  of  right  ascension,  and  thirty 
degrees  south  declination.  Curiosity  respecting  the  object  was 
not,  however,  gratified  until  the  morning  of  June  23d,  when 
it  was  seen  by  observers  in  almost  every  part  of  the  northern 
hemisphere  about  the  beginning  of  the  morning  twilight.  Con- 
tinuing its  northern  course,  it  reached  the  circle  of  perpetual 
apparition  early  in  July,  and  during  the  remainder  of  the 
period  of  its  visibility  neither  rose  nor  set.  Passing  near  the 
north  pole  of  the  heavens,  it  was  visible  all  night  for  several 
weeks.  The  length  of  the  tail  was  variously  estimated,  as  the 
distance  to  which  it  could  be  traced  depended  largely  on  the 
acuteness  of  the  observer's  vision.  To  most  observers  it  pre- 
sented a  length  of  ten  or  fifteen  degrees,  though  sonie  traced 
it  much  farther. 

There  are  two  vei-y  remarkable  features  connected  with  the 
motion  of  this  comet.  One  is,  that  during  almost  its  entire 
period  of  visibility  to  the  naked  eye  it  moved  on  the  same 
meridian  as  the  sun,  and,  indeed,  while  passing  from  the  south- 
ern to  the  northern  hemisphere,  it  may  have  passed  over  the 
sun's  disk.  The  other  feature  is  the  remarkable  resemblance 
between  its  orbit  and  that  of  the  comet  of  1807.  It  was  this 
resemblance  which  led  Dr.  Gould  to  telegraph  it  as  a  return 
of  this  comet.  The  most  careful  determination  of  the  ele- 
ments show,  however,  that  the  two  bodies  could  not  possibly 
be  identical,  as  both  were  moving  in  orbits  differing  so  little 
from  a  parabola  that  many  centuries  at  least  must  elapse  be- 


THE  GREAT  COMET  OF  1882.  391 

fore  the  return  of  either.  We  have,  therefore,  another  case 
similar  to  that  of  the  great  comets  of  1843  and  1880 — namely, 
two  different  bodies  following  each  other  in  neaily  the  san)e 
orbit. 

The  Great  Comet  of  1882.— Early  in  September,  1882,  a 
comet  was  seen  with  the  naked  eye  by  observers  at  the  Cape 
of  Good  Hope,  in  Australia,  and  in  Cordoba,  South  America. 
Dr.  Gill,  at  the  Cape,  describes  it  as  being,  on  September  7th, 
the  date  of  its  first  observation  at  that  point,  a  quite  conspicu- 
ous object,  the  nucleus  appearing  to  the  naked  eye  as  a  star  of 
the  third  magnitude.  On  the  afternoon  of  Sunday,  September 
17th,  the  comet  was  visible  in  broad  daylight,  near  the  sun,  be- 
ing, in  fact,  seen  in  both  hemispheres.  In  the  afternoon  it  was 
evidently  approaching  the  sun's  limb,  and  about  to  perform  a 
transit  over  the  sun's  disk,  similar  to  that  of  Venus.  This 
phenomenon  was  one  previously  unheard  of  in  astronomy,  and 
was,  therefore,  of  the  most  absorbing  interest,  especially  as  it 
would  furnish  the  means  of  determining  whether  the  nucleus 
of  the  comet  was  an  opaque  solid. 

Unfortunately,  the  afternoon  was  far  advanced,  and  it  be- 
came doubtful  whether  the  transit  would  not  commence  too 
late  to  be  seen  at  the  Cape.  Dr.  Gill,  therefore,  sent  a  de- 
spatch to  the  telegraph-otfice  to  apprise  the  astronomers  of  Eng- 
land and  America,  but,  through  some  unexplained  failure,  it 
did  not  reach  them.  As  little  more  than  the  bare  existence 
of  the  object  was  then  known  in  the  northern  hemisphere,  no 
one  thought  of  looking  for  the  phenomenon. 

But,  at  the  Cape,  just  before  the  sun  was  hidden  behind 
Table  Mountain,  two  of  the  observers,  Mr.  Finlay  and  Dr.  El- 
kin,  saw  the  comet  enter  upon  the  sun's  disk.  By  keeping  the 
sun's  limb  at  the  edge  of  the  field,  the  former  was  able  to  fol- 
low the  comet  right  into  the  limb.  He  lost  sight  of  it  sud- 
denly at  4  hours  50  minutes  58  seconds  Cape  mean  time,  when 
it  was  just  entering  upon  the  disk;  but  on  examining  the  disk 
very  carefully,  not  the  slightest  trace  of  the  comet  could  be 
seen.  The  definition  was  bad,  and  in  a  few  minutes  more  the 
sun  disappeared  behind  the  mountain. 
S 


392  THE  SOLAR  SYSTEM. 

Dr.  Elkin's  observation  was  in  all  respects  similar  to  Mr. 
Finlay's.  With  one  of  the  half-lenses  of  the  heliometer  he 
actually  observed  the  comet  to  disappear  among  the  undula- 
tions of  the  sun's  limb  at  4  hours  50  minutes  52  seconds.  The 
intrinsic  brilliancy  of  the  nucleus  seemed  scarcely  inferior  to 
that  of  the  sun's  surface.  It  will  be  seen  that  the  two  ob- 
servers, who  M'cre  entirely  separate  from  each  other,  only  dif- 
fered 6  seconds  in  the  time  of  the  comet's  entry  upon  the  limb. 

The  fact  that  no  trace  of  the  comet  was  visible  upon  the 
face  of  the  sun  after  entering  upon  it  is  of  the  greatest  inter- 
est, as  showing  that  the  solid  opaque  nucleus,  if  it  existed  at 
all,  must  have  been  much  smaller  than  the  apparent  nucleus 
measured  with  the  telescope.  The  transit  of  a  great  comet  like 
this  over  the  sun's  face  is  a  phenomenon  which  cannot  be  ex- 
pected more  than  once  in  many  centuries.  We  must,  therefore, 
congratulate  ourselves  that  two  observers  were  able  to  note  it, 
even  under  very  unfavorable  circr.mstances. 

After  passing  the  perihelion  the  comet  developed  into  the 
most  brilliant  one  which  had  been  seen  for  twenty  years.  It 
had,  however,  a  feature  of  yet  greater  interest  than  its  brill- 
iancy. Wlien  its  orbit  was  calculated,  it  was  found  to  be  al- 
most identical  with  that  of  the  great  comets  of  1843  and  1880. 
The  possibility  that  the  three  bodies  were  identical  gave  rise 
to  a  startling  speculation.  The  diminution  of  the  period  from 
38  years  to  20  months  would  indicate  that  the  comet,  in  pass- 
ing so  near  the  surface  of  the  sun,  met  with  some  resistance, 
the  result  of  which  would  be  that,  continually  shortening  its 
time  of  revolution,  it  would,  in  a  few  years,  fall  into  the  sun. 
Further  computations  show,  however,  that  the  bodies  could  not 
possibly  be  identical,  since  the  comet  flew  away  from  the  sun 
with  a  speed  that  showed  it  must  have  been  many  j-ears  falling 
to  the  sun,  and  centuries  more  before  it  could  again  return. 

Return  of  the  Great  Comet  of  1812. — The  recent  return 
of  this  comet  is  mainly  of  interest  as  showing  the  wonderful 
degree  of  precision  which  modern  astronomy  has  reached. 
On  calculating  its  orbit,  it  was  found  that  its  momentum 
would  carry  it  out  to  near  the  orbit  of  Neptune,  and  that  it 


ENCEE'S   COMET,  AND   THE  BESISTING  MEDIUM.       393 

would  return  in  about  71  years.     It  was  actually  found  by 
Brooks  in  September,  1883,  the  very  year  of  the  prediction. 

Return  of  Olbers'  Comet  of  1815. — Bessel  found  that  this 
comet  had  a  period  of  74  years.  It  actually  returned  in  1887, 
and  was,  like  the  preceding  one,  first  seen  by  Brooks.  The 
discovery  was  made  on  August  24th,  1887,  but  the  comet  did 
not  complete  its  revolution  until  October  6th,  1887. 

§  4.  Enck^s  Comet,  and  the  Resisting  Medium. 

The  comet  which  in  recent  times  has  most  excited  the  atten- 
tion of  astronomers  is  that  known  as  Encke's,  from  the  astron- 
omer who  first  carefully  investigated  its  motion.  It  was  first 
seen  in  January,  1786,  but  the  observations  only  continued 
through  two  days,  and  were  insufiicient  to  determine  the  orbit. 
In  1795  a  comet  was  found  by  Miss  Caroline  Herschel,  on 
which  observations  were  continued  about  three  weeks;  but  no 
very  accurate  orbit  was  dei'ived  fi'om  these  observations.  In 
1805  the  same  comet  returned  again  to  perihelion,  l)ut  its  iden- 
tity again  failed  to  be  recognized.  As  in  the  previous  returns, 
the  observations  continued  through  less  than  a  month.  It  was 
found,  for  the  fourth  time,  by  Pons,  of  Marseilles,  in  1818. 
When  its  orbit  was  calculated,  it  was  seen  to  coincide  so 
closely  with  that  of  the  comet  of  1805  as  to  leave  no  doubt 
that  the  two  were  really  the  same  body. 

The  motions  of  the  comet  were  now  taken  up  by  Encke,  of 
Berlin,  and  investigated  with  a  thoroughness  before  unknown. 
He  found  the  period  to  be  about  1200  days,  four  complete 
revolutions  having  been  made  between  1805  and  1818.  Know- 
ing this,  there  was  no  longer  any  difficulty  in  identifying  the 
comet  of  1795  as  also  being  the  same,  three  complete  revolu- 
tions having  been  made  between  that  date  and  1805.  In  the 
intermediate  returns  to  perihelion,  its  position  had  been  so 
unfavorable  that  it  had  not  been  observed  at  all.  This  result 
was  received  by  astronomers  with  the  greatest  interest,  because 
it  was  the  first  known  case  of  a  comet  of  short  period.  Its  re- 
turn in  1822  was  duly  predicted,  but  it  was  found  that  when 
near  its  greatest  brilliancy  it  would  be  visible  only  in  the 


394:  THE  SOLAR  SYSTEM. 

southern  liemispbere.  Happily,  Sir  Thomas  Brisbane  had  an 
observatory  at  Paramatta,  Xew  South  Wales,  and  his  assistant, 
Riiinker,  was  so  fortunate  as  to  fiud  the  comet.  It  was  so 
near  the  position  predicted  by  Encke  that,  by  constantly  point« 
ing  the  telescope  in  the  direction  predicted  by  that  astronomer, 
the  comet  was  in  the  field  of  view  during  its  whole  course. 

Encke  continued  to  investigate  the  coni-se  of  the  comet  dur- 
ing each  revolution  up  to  the  time  of  his  death,  in  1865.  At 
some  returns  it  could  not  be  seen,  owing  to  its  distance  from 
the  earth,  or  the  otherwise  unfavorable  position  of  our  planet ; 
but  generalU'  very  accurate  observations  of  its  course  were 
made.  By  a  comparison  of  its  motions  with  those  which 
would  result  from  the  gravitation  of  the  sua  and  planets,  he 
found  that  the  periodic  time  was  constantly  diminisliing,  and 
was  thus  led  to  adopt  the  famous  hypothesis  of  Oibers,  that 
the  comet  met  with  a  resisting  medium  in  space.  The  dimi- 
nution of  the  period  was  about  two  hours  and  a  half  in  each 
revolution.  The  conclusion  of  Encke  and  Oibers  was  that  the 
planetary  spaces  are  tilled  with  a  very  rare  medium — so  rare 
that  it  does  not  produce  the  slightest  effect  on  the  motion  of 
such  massive  bodies  as  the  planets.  The  comet  being  a  body 
of  extreme  tenuity,  probably  far  lighter  than  air,  it  might  be 
affected  by  such  a  medium.  The  existence  of  this  medium 
cannot,  however,  be  considered  as  established  by  Encke's  re- 
searches. In  the  first  place,  if  we  grant  the  fact  that  the 
time  of  revolution  is  continually  diminishing,  as  maintained 
by  the  great  German  astronomer,  it  does  not  follow  that  a  re- 
sistinc;  medium  is  the  only  cause  to  which  we  can  attribute  it. 
But  the  main  point  is,  that  the  computations  on  wliicli  Encke 
founded  his  hypothesis  are  of  such  intricacy  as  to  be  alwaj-s 
liable  to  small  errors,  and  their  results  cannot  be  received 
with  entire  confidence  until  some  one  else  has  examined  the 
subject  by  new  and  improved  methods. 

Such  an  examination  was  commenced  some  years  ago  at  the 
Pulkowa  observatory  by  Dr.  von  Asten,  and  since  the  death  of 
that  astronomer  has  been  continued  by  his  successor,  Dr.  Back- 
lund.     The  work  was  devoted  more  especially  to  a  very  care- 


ENCKE'S    COMET,  AND  THE  RESISTING  MEDIUM.      395 

ful  calculation  of  the  action  of  all  the  planets  on  the  comet 
from  1861  to  1878,  a  period  of  live  revolutions  of  the  comet. 
At  first  it  was  thought  there  was  no  retardation  from  1865  to 
1871 ;  but  this  conclusion  was  traced  to  an  error  in  some  of 
the  complicated  calculations  necessary,  and  now  it  is  estab- 
lished that  the  retardation  of  the  comet  goes  on  regularly  from 
one  period  to  another,  so  that  after  a  great  number  of  centu- 
ries have  elapsed  the  comet  must  fall  into  the  sun.  But  long 
before  that  time  the  comet  will  probably  disappear  entirely,  as 
Biela's  comet  has  already  done. 

It  cannot  be  determined  whether  the  comet  is  resisted  at 
every  point  of  its  orbit,  or  only  when  near  the  sun,  but  the 
preponderance  of  evidence  favors  the  latter  result. 

To  judge  whether  the  deviations  in  the  motion  of  Encke'a 
comet  are  really  due  to  a  resisting  medium,  we  should  know 
whether  the  motions  of  other  comets  exhibit  similar  anom- 
alies. So  far  as  is  yet  known,  no  other  one  does.  There  is 
at  least  one  which  h  returned  a  sufficient  number  of  times, 
and  of  which  the  motions  have  been  computed  with  sufficient 
care,  to  lead  to  an  entirely  definite  conclusion  on  this  point, 
namel}^,  the  periodic  comet  of  Faye,  which  has  been  investi- 
gated by  Moller.*  This  comet  was  discovered  in  1813  by  the 
astronomer  whose  name  it  bears,  and  was  soon  found  to  move 
in  an  elliptic  orbit,  with  a  period  of  a  little  more  than  seven 
years.  As  it  has  been  observed  at  several  returns  since,  Moller 
investigated  its  motions  with  a  view  of  finding  whether  its 
period  was  affected  by  any  resisting  medium.  x\t  first  he 
thought  there  was  such  an  effect,  his  general  result  being  of 
the  same  nature  with  that  reached  by  Encke.  But  on  repeat- 
ing his  calculations  with  the  improved  data  afforded  by  a  first 
calculation,  he  found  that  the  result  arose  from  the  imperfec- 
tion of  the  latter,  and  that  the  comet  really  showed  no  sign  of 
a  change  in  its  mean  motion.  It  therefore  seems  certain  that, 
if  there  is  a  resisting  medium,  it  docs  not  extend  out  far 
enough  from  the  sun  to  meet  the  orbit  of  Faye's  comet. 

*  Fiofessoi-  Axel  Moller,  director  of  the  observatory  at  Lund,  Sweden. 


396  THE  SOLAR  SYSTEM. 

§  5.  Other  Periodic  Comets. 

Among  recent  cometary  discoveries  the  first  place  in  inter- 
est niiist  be  assigned  to  Mr.  S.  C.  Chandler's  work  identifying 
a  comet  discovered  by  Brooks  in  1889  with  the  celebrated 
comet  of  Lexell.  The  latter  was  discovered  in  June,  1770, 
and  was  visible  to  the  naked  eye.  Much  to  the  surprise  of 
the  astronomers,  it  was  found  to  be  moving  in  an  elliptic  orbit 
with  a  period  of  only  six  years.  It  also  passed  so  near  the 
orbit  of  the  earth  as  to  frighten  many  lest  there  should  be 
a  collision  which  might  greatly  damage  our  planet.  The 
mystery  of  its  appearance  was  solved  when  it  was  found  that 
it  had  just  come  from  the  neighborhood  of  the  planet  Jupiter ; 
which  had,  presumably,  thrown  it  into  an  entirely  new  orbit. 
On  the  second  revolution  following  it  again  encountered 
Jupiter,  and  its  orbit  was  so  changed  that  it  was  not  again 
seen.  When  the  orbit  of  Brooks's  comet  of  1889  was  com- 
puted, it  was  found  to  be  moving  in  an  orbit  M'ith  a  period  of 
less  than  eight  years ;  and  when  the  case  was  investigated,  it  was 
found  that  the  comet  had  just  come  from  an  encounter  with  Ju- 
piter. Moreover,  this  encounter  took  place  at  the  same  point 
of  Jupiter's  orbit  where  the  planet  met  Lexell's  comet  110 
years  before.  On  computing  back  the  action  of  Jupiter  on 
the  comet,  the  latter  was  found  to  have  been  moving  in  an  or- 
bit wholly  outside  of  that  of  Jupiter.  Although  a  very  strong 
presumption  in  favor  of  the  identity  of  the  two  comets  is  thus 
shown,  further  researches  are  required  before  it  is  proved. 

Of  periodic  comets  seen  at  only  one  return,  many  have  pe- 
riods so  long  that  no  especial  interest  attaches  to  the  ellipticity 
of  the  orbits  at  the  present  time.  In  other  cases  the  observa- 
tions are  so  uncertain  that  great  doubt  attaches  to  the  period. 
The  following  are  cases  in  which  there  is  little  doubt. 

A  comet  which  passed  its  perihelion  on  November  19th, 
1783,  was  found  by  Dr.  C.  H.  F.  Peters  to  have  a  period  of 
less  than  six  years.  But  it  was  never  seen  before  or  since. 
Its  orbit  was  probably  deranged  bj  that  of  Jupiter,  near 
which  it  approaches. 


METEORS  AND  SHOOTING-STARS.  397 

The  comet  of  1812  was  found  by  Encke  to  have  a  period 
of  seventy-one  years,  with  an  uncertainty  of  three  years.  It 
reappeared  in  1883,  as  already  stated. 

The  third  comet  of  1819  was  found  by  Encke  to  have  a 
period  of  five  years  and  seven  months,  but  nothing  more  was 
ever  heard  of  it. 

The  fourth  comet  of  the  same  year  was  found  by  the  same 
computer  to  have  a  period  of  less  than  five  years,  but  it  has 
not  been  seen  again. 

Tlie  fourth  comet  of  1846  has  a  period  of  less  than  one 
hundred  years,  but  it  is  quite  uncertain. 

The  same  year  Dr.  C.  H.  F.  Peters,  at  Naples,  discovered  a 
comet  of  quite  short  period,  which  should  have  returned  sev- 
eral times  before  now;  but  it  has  not  again  been  seen. 

The  same  statement  applies  to  De  Vico's  comet  of  1844. 
Therefore, besides  the  eleven  comets  which  have  actually  been 
observed  at  two  returns,  there  are  but  three  whose  periods  are 
certain. 

The  next  subject  to  which  we  would  ask  the  attention  of 
the  reader  is  that  of  the  physical  constitution  of  comets.  But 
this  subject  can  be  discussed  only  in  connection  with  another, 
to  which,  at  first  sight,  it  seems  to  have  no  relation,  though 
so  curious  a  relation  has  really  been  discovered  as  greatly  to 
modify  our  views  of  what  a  comet  probably  is.  We  refer  to 
the  phenomena  of  meteors,  meteoric  showers,  and  shooting- 
stars,  which  next  claim  our  attention. 

§  6.  Meteors  and  Shooting-stars. 

If  we  carefully  watch  the  heavens  on  a  cloudless  night,  we 
Bhall  frequently  see  an  appearance  as  of  a  star 'rapidly  shoot- 
ing through  a  short  space  in  the  sky,  and  then  suddenly  dis- 
appearing. Three  or  four  such  shooting-stars  may  generally 
be  seen  in  the  course  of  an  hour.  Generally  they  are  visible 
only  for  a  second  or  two,  but  sometimes  move  slowly,  and  are 
seen  much  longer.  Occasionally  they  are  so  brilliant  as  to 
illuminate  the  whole  heavens,  and  they  are  then  known  as 
meteors — a  term  which  is  equally  applicable  to  the  ordinary 


398  THE  SOLAR  SYSTEM. 

shooting-stars.  In  general,  they  are  seen  only  one  at  a  time, 
and  are  so  minute  as  hardl}'  to  attract  attention.  But  they 
have  on  some  occasions  shown  themselves  in  such  numbei"s  as 
to  till  the  beholders  with  terror,  lest  the  end  of  the  world  had 
come.  The  Chinese,  Arabian,  and  other  historians  have  hand- 
ed down  to  us  many  accounts  of  such  showers  of  meteors, 
wliich  have  been  brought  to  light  by  the  researches  of  Edward 
Biot,  Quetelet,  Professor  H.  A.  Newton,  and  others.  As  an  ex- 
ample of  these  accounts, we  give  one  from  an  Arabian  writer: 

"  In  the  year  599,  on  the  last  day  of  Moharrem.,  stars  shot 
hither  and  thither,  and  flew  against  each  other  like  a  swarm 
of  locusts ;  this  phenomenon  lasted  until  daybreak ;  people 
were  thrown  into  consternation,  and  made  supplication  to  the 
Most  High  :  there  was  never  the  like  seen  except  on  the  com- 
ing of  the  messenger  of  God,  on  whom  be  benediction  and 
peace." 

In  1799,  on  the  night  of  November  12th,  a  remarkable 
shower  was  seen  by  Humboldt  and  Bonpland,  who  were  then 
on  the  Andes.  Humboldt  described  the  shower  as  commen- 
cing a  little  before  two  o'clock,  and  the  meteors  as  rising  above 
the  horizon  between  east  and  north-east,  and  moving  over  tow- 
ards the  south.  From  not  continuing  his  observations  long 
enough,  or  from  some  other  cause,  lie  failed  to  notice  that  the 
lines  in  which  the  meteors  moved  all  seemed  to  converge  tow- 
ards the  same  point  of  the  heavens,  and  thus  missed  the  dis- 
covery of  the  real  cause  of  the  phenomenon. 

The  next  great  shower  was  seen  in  this  country  in  1833. 
All  through  the  Southern  States,  the  negroes,  like  the  Arabs  of 
a  previous  century,  thought  the  end  of  the  world  had  come  at 
last.  The  phenomenon  was  observed  very  carefully  at  New 
Haven  by  Professor  Olmsted,  who  worked  out  a  theory  of  its 
cause.  Although  his  ideas  are  in  many  respects  erroneous, 
they  were  the  means  of  suggesting  the  true  theory  to  others. 
The  recurrence  of  the  shower  at  this  time  suggested  to  the 
astronomer  Olbers  the  idea  of  a  thirty -four-year  period,  and 
led  him  to  predict  a  return  of  the  shower  in  1867.  A  few 
years  before  the  expected  time,  the  subject  was  taken  up  by 


METEORS  AND  SHOOTING-STARS.  399 

Professor  Newton,  of  Yale  College,  to  whose  researches  our 
knowledge  of  the  true  cause  of  the  phenomenon  is  very  large- 
\y  due. 

The  phenomena  of  shooting-stars  branch  out  in  yet  another 
direction.  As  we  have  described  thein,  thej'  are  seen  only  iix 
the  higher  and  rai-er  regions  of  the  atmosphere,  far  above  the 
clouds:  no  sound  is  heard  from  them,  nor  does  anything  reach 
the  surface  of  the  earth  from  which  the  nature  of  the  object 
can  be  inferred.  But  on  rare  occasions  meteors  of  extreme 
brilliancy  are  followed  by  a  loud  sound,  like  the  discharge  oi 
heavy  artillery  ;  while  on  yet  rarer  occasions  large  masses  of 
metallic  or  ston}'  substances  fall  to  the  earth.  These  aerolites 
were  the  puzzle  of  philosophers.  Sometimes  there  was  much 
scepticism  as  to  the  reality  of  the  phenomenon  itself,  it  ap- 
pearing to  the  doubters  more  likely  that  those  who  described 
such  things  were  mistaken  than  that  heavy  metallic  masses 
should  fall  from  the  air.  When  their  reality  was  pUiced  be- 
yond doubt,  many  theories  were  propounded  to  account  for 
them,  the  most  noteworthy  of  which  was  that  they  were 
thrown  from  volcanoes  in  the  moon.  The  problem  of  the 
motion  of  a  body  projected  from  the  moon  was  inxestigated 
by  several  great  mathematicians,  the  result  being  tliat  such  a 
body  could  not  reach  the  eartli  unless  projected  with  a  veloci 
ty  far  exceeding  anything  seen  on  our  planet. 

When  aerolites  were  examined  by  chemists  and  mineralo- 
gists, it  was  found  tliat  although  they  contained  no  new  chem- 
ical elements,  yet  the  combinations  of  these  elements  M'ere 
quite  unlike  any  found  on  the  earth,  so  that  they  must  have 
originated  outside  the  earth.  Moreover,  these  combinations 
exhibited  certain  characteristics  peculiar  to  aerolites,  so  that 
the  mineralogist,  from  a  simple  examination  and  analysis  of 
a  substance,  could  detect  it  as  part  of  such  a  body,  though 
it  had  not  been  seen  to  fall.  Great  masses  of  matter  thus 
known  to  be  of  meteoric  origin  have  been  found  in  various 
parts  of  the  earth,  especially  in  Nortliern  Mexico,  where,  at 
some  unknown  period,  an  immense  shower  of  these  bodies 

Beems  to  have  fallen. 

27 


400  .        THE  SOLAR   SYSTEM. 

Cause  of  Shooting-stais. — It  is  now  iinivei-sally  conceded  that 
the  celestial  spaces  are  crowded  witli  iiiniinierable  minute 
bodies  moving  around  the  sun  in  every  possible  kind  of  orbit. 
When  we  say  croM'ded,  we  use  the  word  in  a  relative  sense ; 
they  may  not  average  more  than  one  iu  a  million  of  cubic 
miles,  and  yet  their  total  number  exceeds  all  calculation.  Of 
the  nature  of  the  minuter  bodies  of  this  class  nothiug  is  cer- 
tainly known.  But  whatever  they  may  be,  the  earth  is  con- 
stantly encountering  them  in  its  motion  around  the  sun.  They 
are  burned  by  passing  through  the  upper  regions  of  our  at- 
mosphere, and  the  shooting  -  star  is  simply  the  light  of  that 
burning.  We  shall  follow  Professor  Newton  in  calling  these 
invisible  bodies  meteoroids. 

The  question  which  may  be  asked  at  this  stage  is.  Why  are 
these  bodies  burned  ?  Especialh',  how  can  thej^  burn  so  sud- 
denly, and  with  so  intense  a  light,  as  to  be  risible  hundreds 
of  miles  j.way  ?  These  questions  were  the  stumbling-block  of 
investigators  until  they  were  answered,  clearly  and  conchisive- 
ly,  by  the  discovery  of  the  mechanical  theory  of  heat.  It  is 
now  established  that  heat  is  only  a  certain  form  of  motion ; 
that  hot  air  differs  from  cold  air  only  in  a  more  rapid  vibra- 
tion of  jts  molecules,  and  that  it  communicates  its  heat  to 
other  bodies  simply  by  striking  them  with  its  molecules,  and 
thus  setting  their  molecules  in  vibration.  Consequently,  if  a 
body  moves  rapidly  through  the  air,  the  impact  of  the  air 
upon  it  ought  to  heat  it  just  as  Avarm  air  would,  even  though 
the  air  itself  were  cold.  This  result  of  theory  has  been  ex- 
perimentally proved  by  Sir  William  Thomson,  who  found  that 
a  thermometer  placed  in  front  of  a  rapidly  moving  body  rose 
one  degree  when  the  body  moved  through  the  air  at  the  rate 
of  125  feet  per  second.  With  higher  velocities,  the  increase 
of  temperature  was  proportional  to  the  square  of  the  velocity, 
being  4  degrees  with  a  velocity  of  250  feet,  16  degrees  with 
one  of  500  feet  per  second,  and  so  on.  This  result  is  in  exact 
accordance  with  the  mechanical  theory  of  heat.  To  find  the 
effective  temperature  to  which  a  meteoroid  is  exposed  in  mov- 
ing through  our  atmosphere,  we  divide  its  velocity  in  feet  per 


METEORS  AND  SHOOTING-STARS.  401 

second  by  125  ;  the  square  of  the  quotient  will  give  the  teni- 
perature  in  degrees. 

Let  us  appl}'-  this  principle  to  the  case  of  the  nieteoroids. 
The  earth  moves  in  its  orbit  at  the  rate  of  98,000  feet  pei 
second  ;  and  if  it  met  a  meteoroid  at  rest,  our  atmosphere 
would  strike  it  with  this  velocity.  By  the  rule  we  have  given 
for  the  rise  of  temperature  (98,000 -^  125)=  =  784'=  600,000 
degrees,  nearly.  This  is  many  times  any  temperature  ever 
produced  by  artificial  means.  If,  as  will  commonly  be  the 
case,  the  meteoroid  is  moving  to  meet  the  earth,  the  velocity, 
and  therefore  the  potential  temperature,  will  be  higher.  We 
know  that  the  meteoroids  which  produce  the  IS^ovember  show- 
ers already  described  move  in  a  direction  nearly  opposite  that 
of  the  earth  with  a  velocity  of  26  miles  per  second,  so  that  the 
relative  velocity  with  which  the  meteoroids  meet  our  atmos- 
phere is  44  miles  per  second.  By  the  rule  we  have  given, 
this  velocity  coiTesponds  to  a  temperature  of  between  three 
and  four  million  degrees.  We  do  not  mean  that  the  meteor- 
oids are  actually  heated  up  to  this  temperature,  but  that  the 
air  acts  upon  them  as  if  it  were  heated  up  to  the  point  men- 
tioned ;  that  is,  it  burns  or  volatilizes  them  in  less  than  a  sec- 
ond with  an  enormous  evolution  of  light  and  heat,  just  as  a 
furnace  would  if  heated  to  a  temperature  of  three  million  de- 
grees. It  is  not  at  all  necessary  that  the  body  should  be  com- 
bustible; the  light  and  heat  of  ordinary  burniug  arc  nothing 
at  all  compared  with  the  deflagration  which  such  a  tempera- 
ture would  cause  by  acting  on  the  hardest  known  body.  A 
few  grains  of  platinum  or  iron  striking  the  atmosphere  with 
the  velocity  of  the  celestial  motions  nn'ght  evolve  as  much  light 
and  heat  as  are  emitted  by  the  burning  of  a  pint  of  coal-oil  or 
several  pounds  of  gunpowder ;  and  as  the  whole  operation  is 
over  in  a  second,  we  may  imagine  how  intense  the  light  must  be. 

The  varied  phenomena  of  aerolites,  meteors,  shooting-stars, 
and  meteoric  showers  depend  solely  on  the  number  and  nat- 
ure of  the  meteoroids  which  give  rise  to  them.  If  one  of 
these  bodies  is  so  large  and  firui  as  to  pass  through  the  atmos- 
phere and  reach  the  earth  without  being  destroyed  by  the  po 


402  THE  SOLAR  SYSTEM. 

tential  heat,  we  have  an  aerolite.  As  this  passage  only  occu 
pies  a  few  seconds,  the  heat  has  not  time  to  penetrate  far  into 
the  interior  of  the  body,  but  expends  itself  in  melting  and  vol- 
atilizing the  outer  portions.  When  the  body  lirst  strikes  the 
denser  portion  of  the  atmosphere,  the  resistance  becomes  so 
enormous  thai  the  aerolite  is  frequently  broken  to  pieces  witii 
6uch  violence  that  it  seems  to  explode.  Further  color  is  given 
to  the  idea  of  an  explosion  by  the  loud  detonation  which  fol- 
lows, so  that  the  explosion  is  frequently  spoken  of  as  a  fact, 
and  as  the  cause  of  the  detonation.  Really,  there  is  good  rea- 
son to  believe  that  both  of  these  phenomena  are  due  to  the 
body  striking  the  air  with  a  velocity  of  ten,  twenty,  or  thirty 
miles  a  second. 

If,  on  the  other  hand,  the  meteoroid  is  so  small  or  so  fusible 
as  to  be  dissipated  in  the  upper  regions  of  the  atmosphere,  we 
have  a  common  shooting-star,  or  a  meteor  of  greater  or  less 
brilliancy.  Very  carefid  observations  have  been  made  from 
time  to  time,  with  a  view  of  finding  the  height  of  these  bodies 
above  tlie  earth  at  their  appearance  and  disappearance.  An 
attempt  of  this  kind  was  made  by  the  Xaval  Observatorj-  on 
the  occasion  of  the  meteoric  shower  of  November  13th,  1S67, 
when  Professor  Ilarkness  was  sent  to  Richmond  to  map  the 
paths  of  the  brighter  meteors  as  seen  from  tliat  point.  By 
comparing  these  paths  with  those  mapped  at  AVashington,  the 
Parallaxes,  and  thence  the  altitudes,  of  these  bodies  were  de- 
rermined.  The  lightning-like  rapidity  with  wliicii  the  mete- 
oi-s  darted  through  their  course  rendered  it  impossible  to  ob- 
■icrve  them  with  astronomical  precision  ;  but  the  general  re- 
sult was  that  they  were  first  seen  at  an  average  height  of  75 
miles,  and  disappeared  at  a  height  of  55  miles.  There  wa^ 
no  positive  evidence  that  any  meteor  commenced  at  a  height 
nuch  greater  than  100  miles.  It  is  remarkable  that  this  cor 
responds  very  nearly  to  the  greatest  height  at  whicli  the  most 
brilliant  meteors  are  ever  certainly  seen.  These  phenomena 
seem  to  indicate  that  our  atmosphere,  iiistead  of  terminating 
at  a  height  of  45  miles,  as  was  formerly  supposed,  really  eX' 
tends  to  a  hei^-ht  of  between  100  and  110  miles. 


METEORS  AND  SHOOTING-STABS. 


403 


The  ordinary  meteors,  which  we  may  see  on  every  clear 
evening,  move  in  every  direction,  thus  showing  that  their  or- 
bits lie  in  all  possible  positions,  and  are  seemingly  scattei-ed 
entirely  at  random.  But  the  case  is  qnite  different  with  tliost 
meteoroids  which  give  rise  to  meteoric  showers.  Here  we 
have  a  swarm  of  these  bodies,  all  moving  in  the  same  direc- 
tion in  parallel  lines.     If  we  mark,  on  a  celestial  globe,  the 


Pig.  95.— Meteor  paths,  illustrating  the  radiant  point 


apparent  paths  of  the  meteoi-s  which  fall  during  a  shower,  ot 
if  we  suppose  them  marked  on  the  celestial  sphere,  and  then 
continue  them  backwards,  we  shall  find  them  all  to  meet  in 
the  same  point  of  tlie  heavens.  This  is  called  the  radiant 
point  It  always  appears  in  the  same  position,  wherever  the 
observer  is  situated,  and  does  not  partake  of  the  diurnal  mo 


404  THE  SOLAE  SYSTEM. 

tion  of  the  earth ;  that  is,  as  the  stars  seem  to  move  towards 
tlie  west  in  their  diurnal  course,  the  radiant  point  moves  with 
them.  The  point  in  question  is  purely  an  effect  of  perspeo- 
tive,  being  the  "vanishing  point"  of  tlie  parallel  lines  ia 
whicli  the  meteors  really  move.  These  lines  do  not  appear 
in  their  real  direction  in  space,  but  are  seen  as  projected  on 
the  celestial  sphere.  A  good  visible  illustration  of  the  effect 
in  question  may  be  afforded  by  looking  upwards  and  watch- 
ino-  fallins  snow  durinor  a  calm.  Tlie  flakes  which  are  fall- 
ing  directly  towards  the  observer  do  not  seem  to  move  at  all, 
while  the  surrounding  flakes  seem  to  separate  from  them  on 
all  sides.  So  with  the  meteoric  showei-s.  A  meteor  coming 
directly  towards  the  observer  does  not  seem  to  move  at  all^ 
and  marks  the  radiant  point  from  which  all  the  othei-s  seem 
to  diverge.  The  great  importance  of  the  determination  of 
the  radiant  point  arises  from  the  fact  that  it  marks  the  direc- 
tion in  which  the  meteors  are  moving  relatively  to  the  eaith, 
and  thus  affords  some  data  for  detei-mining  their  orbits. 

§  7.  Relations  of  Comets  and  Meteoroids. 

We  have  now  to  mention  a  series  of  investigations  which 
led  to  the  discovery  of  a  curious  connection  between  meteor- 
oids and  comets.  These  investigations  were  commenced  by 
Professor  Kewton  on  the  November  meteoi-ic  showers.  Tra- 
cing back  the  historical  accounts  of  these  showers  to  which 
we  have  already  alluded,  he  found  that  the  thirty-three-year 
period,  which  had  been  suspected  by  Olbers,  was  confirmed  by 
records  reaching  back  a  thousand  years.  Moreover,  the  show- 
ers in  question  occurred  only  at  a  certain  time  of  the  year:  in 
1799  and  1833,  it  was  on  November  12th  or  November  13th 
In  other  words,  the  shower  occurred  only  as  the  earth  passed 
a  certain  point  of  its  orbit.  But  this  point  was  found  not  lo 
be  alwavs  the  same,  the  showers  being  found  to  occur  about 
a  couple  of  days  earlier  every  century  as  they  were  traced 
back.  The  principal  conclusions  to  which  these  facts  led 
were  as  follows : 

1.  That  the  swarm  of  meteoroids  which  cause  the  Novem- 


BELATIONS  OF  COMETS  AND  METEOROIDS.  405 

ber  showers  revolve  around  the  sun  in  a  definite  orbit,  which 
intersects  the  orbit  of  the  earth  at  the  point  which  the  latter 
now  passes  on  November  13th. 

2.  The  point  of  intersection  of  the  two  orbits  moves  for- 
wards about  52"  per  annum,  or  nearly  a  degree  and  a  half  a 
century,  owing  to  a  change  in  the  position  of  the  meteoric 
orbit. 

3.  The  swarm  of  meteoroids  is  not  equally  scattered  all 
around  their  orbit,  but  the  thickest  portion  extends  along 
about  one-fifteenth  of  the  orbit. 

4.  The  earth  meets  this  swarm,  on  the  average,  once  in 
33.25  years.  At  other  times  the  swarm  has  not  arrived  at 
the  point  of  crossing,  or  has  already  passed  it,  and  a  meteoric 
shower  cannot  occur  unless  the  earth  and  the  swarm  cross  at 
the  same  tinie. 

Professor  Newton  did  not  definitely  determine  the  time  of 
revolution  of  the  meteors  in  their  orbit,  but  showed  that  it 
must  have  one  of  five  values.  The  greatest  of  these  values, 
and  the  one  which  it  seems  most  natural  to  select,  is  that  of 
the  mean  interval  between  the  showers,  or  33^  years.  Adopt- 
ing this  pei-iod,  it  would  follow  that  between  1799,  when 
Humboldt  saw  the  meteoric  shower,  and  1833,  when  it  was 
seen  throughout  the  United  States,  the  swarm  of  meteoroids 
had  been  fiying  out  as  far  as  the  planet  Uranus  in  a  very  el- 
liptical orbit,  and  returning  again.  But  the  periodic  time 
might  also  be  one  year  and  about  eleven  days.  Then  the 
group  which  Humboldt  saw  on  November  12th,  1799,  would 
not  reach  the  same  point  of  its  orbit  until  November  23d, 
1800,  when  the  earth  would  have  passed  by.  Passing  11  days 
later  every  year,  it  would  make  about  33  revolutions  in  34 
years,  and  thus  would  pass  about  the  middle  of  November 
once  more,  and  another  shower  would  occur.  In  a  word,  giv- 
ing exact  numbers,  we  might  suppose  that  in  the  period  of 
33^  years  the  meteoroids  made  one  revolution,  or  32|^,  34J, 
65^,  or  Cuh  revolutions,  and  the  conditions  of  the  problem 
would  be  equally  satisfied. 

At  the  same  time,  Professor  Newton  gave  a  test  by  which 


406  THE  SOLAR  SYSTEM. 

the  trne  time  could  be  determined.  As  we  have  said,  he 
showed  that  the  node  of  the  orbit  changed  its  position  52"  a 
century,  and  there  could  be  no  doubt  that  this  change  was 
due  to  the  attraction  of  the  planets.  If,  tlien,  the  effect  of 
this  attraction  was  calculated  for  each  of  the  live  orbits,  it 
would  be  seen  which  of  them  would  give  the  required  change. 
This  was  done  by  Professor  Adams,  of  England,  and  the  result 
was  that  the  thirty-three-year  period,  and  that  alone,  was  ad- 
missible. 

These  researches  of  Professor  Kewton  were  published  in 
1864,  and  ended  with  a  prediction  of  the  return  of  the  shower 
on  ISTovember  13th  of  one  or  more  of  the  three  following 
years — probably  1866.  This  prediction  was  verified  by  a  re- 
markable meteoric  shower  seen  in  Europe  on  that  very  day, 
which,  however,  was  nearly  over  before  it  could  become  visi- 
ble in  this  country.  On  the  same  date  of  the  year  following, 
a  shower  was  visible  in  this  country,  and  excited  great  public 
interest.  From  the  data  derived  from  the  first  of  these  show- 
ers, Schiaparelli,  an  Italian  astronomer,  was  led  to  the  discovery 
of  a  remarkable  relation  between  meteoric  and  cometary  orbits. 
Assuming  the  period  of  the  Xovember  meteoroids  to  be  33^ 
years,  he  computed  the  elements  of  their  orbit  from  the  ob- 
served position  of  the  I'adiant  point.  A  similar  computation 
was  made  by  Leverrier,  and  the  results  were  presented  to  the 
French  Academy  of  Sciences  on  January  21st,  1867. 

The  exact  orbit  which  these  bodies  followed  through  space, 
crossing  the  earth's  orbit  at  one  point,  and  extending  out 
beyond  the  planet  Uranus  at  another,  was  thus  ascertained. 
But,  as  these  bodies  were  absolutely  invisible,  no  great  inter* 
est  seemed  to  attach  to  their  orbit  until  it  was  found  that  a 
comet  was  moving  in  that  very  orbit.  This  was  a  faint  tele- 
scopic comet  discovered  by  Tempel,  at  Marseilles,  in  Decem- 
ber, 1865.  It  was  afterwards  independently  discovered  by 
Mr.  H.  P.  Tuttle,  at  the  Xaval  Observatory,  Washington.  It 
passed  its  perihelion  in  January,  and,  receding  from  the  sun, 
vanished  from  sight  in  March.  It  Avas  soon  found  to  move 
in  an  elliptic  orbit,  but,  owing  to  the  uncertainty  of  observa* 


RELATIONS  OF  COMETS  AND  METEOROIDS. 


407 


tions  on  sncli  a  body, 
there  was  at  tirst  some 
disagreement  as  to  the 
exact  periodic  time. 
The  subject  was  taken 
up  by  Dr.  Oppolzer,  of 
Vienna,  who,  in  Janu- 
ary, 1867,  was  able  to 
present  a  definitive  or- 
bit of  the  comet,  which 
was  published  in  the  ^s- 
tronomische  Nachrichten 
on  the  28th  of  that 
month.  We  now  pre- 
sent the  orbit  of  the 
comet,  as  found  by  Op- 
polzer, and  that  of  the 
meteors,  as  found  by 
Leverrier,  premising 
that  these  orbits  were 
computed  and  publish- 
ed within  a  few  days 
of  each  other,  Avithout 
any  knowledge  on  the 
part  of  either  astronomer  of  the  results  obtained  by  the  other: 


Pig.  96. — Orbit  of  November  meteors  and  the  comet 
of  1S61. 


Thu  Comet. 

MeteoroidB. 

Period  of  revolution 

33.18  vrs. 

0.90.54 

0.9765 

162°  42' 

51°  26' 

42°  24' 

33.25  yrs. 

0.9044 

0.9890 

165°  19' 

51°  18' 

Near  node. 

Eccentricitv 

Perihelion  distance 

Inclination  of  orbit 

Longitude  of  the  node 

Longitude  of  perihelion 

The  similarity  of  these  orbits  is  too  striking  to  be  the  result 
of  chance.  The  only  element  of  which  the  values  differ  ma- 
terially is  the  inclination,  and  this  difference  proceeds  from 
Leverrier  not  having  used  a  very  exact  position  of  the  radiant 
point  in  making  his  computations.  Professor  Adams  found 
by  a  similar  calculation  that  the  inclination  of  the  orbit  of  the 


40S 


THE  SOLAR  SYSTEM. 


meteoroids  was  163°  14',  ouly  half  a  degree  different  from  that 
of  the  orbit  of  Tempers  comet.  The  result  of  these  investiga- 
tions was  as  follows : 

T/ie  November  meteoric  showers  arise  from  the  earth  encountenng 
a  swaj'in  of  2'><^i'ticles  following 
TempeTs  comet  in  its  orbit. 

"When  this  fact  came  out, 
Scliiaparelli  had  been  working 
on  the  same  subject,  and  had 
come  to  a  similar  conclusion 
with  regard  to  another  group 
of  meteors.  It  had  long  been 
known  that  about  August  9th 
of  every  year  an  unusual  num- 
ber of  meteors  shoot  forth  from 
the  constellation  Pei"seus.  At 
times  these  showere  have  been 
inferior  only  to  those  of  Xo- 
vember.  Thus,  on  August  9th, 
1798,  they  succeeded  each  otli- 
er  so  rapidly  as  to  keep  the 
eye  of  the  observer  almost  con- 
stantly engaged,  and  several 
hundred  may  nearly  always  be 
counted  on  the  nights  of  the 
9th,  10th,  and  11th.  These 
August  meteors  are  remarka- 
ble in  that  they  leave  trails  of 
luminous  vapor  which  often 
last  several  seconds.  Assum- 
ing the  orbit  of  this  group  to 
be  a  parabola,  it  was  calculated 
by  Schiaparelli,  and  is  substan- 
tially the  same  with  that  of  a 
comet  observed  in  1862.  The 
following  are  the  elements  of 

the  orbits  of  the  two  bodies:         no.  97— Orblt  of  the  second  comet  of  1S«2. 


BELATIONS  OF  COMETS  AND  METEOltOIDS. 


409 


Comet  11., 
186-2. 

AuffUSt 

MeteoroidB. 

Perihelion  distance 

Inclination  of  orbit 

Longitude  of  t!ie  node 

Longitnde  of  the  })eiiiielion 

0.9626 
113°  85' 
137°  27' 
344°  41' 

0.9643 
115°  57' 
138°  16' 
343°  28' 

It  appears  that  the  x\ngust  meteors  are  caused  b^^  a  long 
stream  of  bodies  following  the  second  comet  of  1862  in  its 
orbit,  or,  rather,  moving  in  the  same  orbit  with  it.  The  orbit 
of  this  comet  is  decidedly  elliptic;  the  difference  from  the 
parabola  is,  however,  too  small  to  be  determined  with  great 
precision.  According  to  Oppolzer,  the  period  derived  from 
'tlie  observations  wonld  be  124  veal's,  which,  however,  may  be 
ten  years  or  more  in  error. 

A  third  striking  case  of  the  connection  between  comets  and 
meteors  which  we  are  showing  is  afforded  by  the  actual  pre- 
diction of  a  meteoric  shower  on  the  night  of  November  27th, 
1872.  I  have  already  described  Biela's  comet  as  first  break- 
ing into  two  pieces  and  then  entirely  disappearing,  as  though 
its  parts  had  become  completely  scattered.  This  is  one  of 
the  few  comets  which  may  come  ver^'  near  the  earth,  the  lat- 
ter passing  the  orbit  of  the  comet  on  November  27tli  of  each 
year.  By  calculation,  the  comet  should  have  passed  the  ])oint 
of  crossing  early  in  September,  1872,  while  the  earth  reached 
the  same  point  between  two  and  three  months  later.  Judg- 
ing from  analogy,  there  was  every  reason  to  believe  that  the 
earth  would  encounter  a  stream  of  meteoroids  consisting  of  the 
remains  of  the  lost  comet,  and  tliat  a  small  meteoric  shower 
wonld  be  the  result.  Moreover,  it  was  shown  that  the  mete- 
ors would  all  diverge  from  a  certain  point  in  the  constellation 
Andromeda,  as  the  radiant  point,  because  that  would  be  the  di- 
rection from  which  a  body  moving  in  the  orbit  of  the  comet 
would  seem  to  come.  The  prediction  was  fully  verified  in 
every  respect.  The  meteors  did  not  compare,  either  in  num- 
bers or  brilliancy,  with  the  great  dis])lays  of  November;  but. 
though  faint,  they  succeeded  each  other  so  rapidly  that  the 
most  casual  observer  could  not  fail  to  notice  them,  and  they 
all  moved  in  the  uredicted  direction. 


410  TRE  SOLAR  SYSTEM. 

That  the  meteoroids  in  these  cases  originally  belonged  to 
the  com.et,  few  will  dispute.  Accepting  this,  tlie  phenomena  cf 
tlie  November  showers  lead  to  the  conclusion  that  the  comet 
of  1SG6,  with  wliich  they  are  associated,  was  not  an  original 
member  of  onr  system,  but  has  been  added  to  it  within  a 
time  whicli,  astronomically  speaking,  is  still  recent.  The  sep- 
ai'ate  meteoroids  which  form  the  stream  will  necessarily  have 
slightly  different  periodic  times.  Such  being  the  case,  they 
will,  in  the  course  of  man}'  revolutions,  gradually  scatter  them- 
selves around  their  entire  orbit ;  and  then  we  shall  have  an 
equal  meteoric  shower  on  every  13th  of  November.  This 
complete  scattering  seems  to  liave  actually  taken  place  in  the 
case  of  the  August  meteoroids,  since  we  have  nearly  the  same 
sort  of  shower  on  every  9th  or  lUlh  of  August.  But  in  the 
case  of  the  November  meteors,  the  stream  is  not  yet  scattered 
over  one-tenth  of  the  orbit.  If  we  suppose  that  tlie  motions 
of  the  slowest  and  the  swiftest  bodies  of  the  stream  only  dif- 
fer by  a  thousandtli  part  of  their  whole  amount — which  is  not 
an  unreasonable  supposition — it  would  follow  that  the  stream 
had  only  made  about  100  revolutions  around  the  sun,  and  had 
therefore  been  revolving  only  about  3300  years.  Though  this 
number  is  purely  hv'pothetical,  we  may  say  with  confidence 
that  the  stream  has  not  been  in  existence  many  thousand 
years. 

This  opinion  is  strongly  supported  by  the  fact  that  the  orbit 
of  this  meteoric  comet  passes  very  near  that  of  Ui-anus  as  v/ell 
as  that  of  the  earth,  so  that  there  is  reason  to  believe  that  it 
was  introduced  into  our  system  by  the  attraction  of  one  of 
these  planets,  probably  of  Uranus.  If  the  comet  is  seen  on  its 
next  return,  in  1899,  we  may  hope  that  its  periodic  time  \vili 
be  determined  with  sufficient  accuracy  to  enable  us  to  fix  with 
some  probability  the  exact  date  at  which  LTranus  brought  it 
into  our  system.  Indeed,  Leverrier  has  attempted  to  do  this 
already,  having  fixed  upon  the  year  126  of  our  era  as  the 
probable  date  of  this  event ;  but,  unfortunately,  neither  the 
position  of  the  orbit  nor  the  time  of  revolution  is  yet  known 
with  such  accuracy  as  to  inspire  confidence  in  this  result. 


THE  PHYSICAL   CONSTITUTION  OF  COMETS.  411 

The  idea  that  this  November  group  is  something  compara 
tively  new  is  strengthened  by  a  comparison  with  tliat  which 
produces  the  August  meteors,  whei-e  we  iind  a  decided  mark 
of  antiquity.  Here  the  swiftest  of  the  group  has,  in  the  course 
of  numerous  revohitions,  overtaken  the  slowest,  so  that  the 
group  is  now  spread  ahnost  equally  aromid  the  entire  orbit. 
The  time  of  revolution  being,  in  tiiis  case,  more  than  a  cen- 
tury, this  equal  distribution  would  take  a  much  longer  time 
than  in  the  other  case,  where  the  period  is  only  thirty-three 
years;  so  that  we  can  say,  with  considerable  probability,  that 
the  August  group  has  been  in  our  system  at  least  twenty 
times  as  long  as  the  November  group. 

§  8.  The  Physical  Constitution  of  Comets. 

A  theory  of  the  physical  constitution  of  comets,  to  be  both 
complete  and  satisfactory,  must  be  founded  on  the  properties 
of  matter  as  made  known  to  us  here  at  the  surface  of  the 
earth.  That  is,  we  must  show  what  forms  and  what  combina- 
tions of  known  substances  would,  if  projected  into  the  celes- 
tial spaces,  present  the  appearance  of  a  comet.  Now,  this  has 
never  yet  been  completely  done.  Theoi'ies  without  number 
have  been  propounded,  but  they  fail  to  explain  some  of  the 
phenomena,  or  explain  them  in  a  manner  not  consistent  with 
the  known  laws  of  matter  or  force.  We  cannot  stop  even  to 
mention  most  of  these  theories,  and  shall  therefore  confine  our 
attention  to  those  propositions  which  are  to  some  extent  sus- 
tained by  facts,  and  which,  on  the  whole,  seem  to  have  most 
probability  in  their  favor. 

The  simplest  form  of  these  bodies  is  seen  in  the  telescopic 
comets,  which  consist  of  minute  particles  of  a  cloudy  or  vapur- 
ous  appearance.  Now,  we  know  that  masses  which  present 
tliio  appearance  at  the  surface  of  the  earth,  where  we  can  ex- 
amine them,  are  composed  of  detached  particles  of  solid  or 
liquid  matter.  Clouds  and  vapor,  for  instance,  are  composed 
of  minute  drops  of  water,  and  smoke  of  very  minute  particles 
of  carbon.  Analogy  would  lead  us  to  suppose  that  the  tele- 
scopic comets  ai'c  of  "Jie  same  constitution.     They  are  gener 


412  THE  SOLAR  SYSTEM. 

ally  tens  of  thousands  of  miles  in  diameter,  and  yet  of  such 
tenuity  that  the  smallest  stars  are  seen  through  them.  The 
strongest  evidence  of  this  constitution  is,  however,  afforded  by 
tlie  phenomena  of  meteoric  showers  described  in  the  last  sec- 
tion. We  have  seen  that  these  are  caused  by  our  atmosphere 
encountering  the  debris  of  comets,  and  this  debris  presents  it- 
self in  the  form  of  -detached  meteoroids,  of  verv  small  magrni-' 
tnde,  but  hundreds  of  miles  apart. 

The  only  alternative  to  this  theory  is  that  the  comet  is  a 
mass  of  true  gas,  continuous  throughout  its  whole  extent. 
This  gaseous  theory  derives  its  main  support  from  the  spec- 
troscope, which  shows  the  spectrum  of  the  telescopic  comets 
to  consist  of  bright  bands,  the  mark  of  an  incandescent  gas. 
Moreover,  the  i-esemblance  of  these  bands  to  those  produced 
by  the  vapor  of  cai'bon  is  so  striking  that  it  is  quite  common 
among  spectroscopists  to  speak  of  a  comet  as  consisting  of 
the  gas  of  some  of  the  compounds  of  carbon.  But  there  are 
several  difficulties  which  look  insuperable  in  the  way  of  the 
theory  that  a  comet  is  nothing  but  a  mass  of  gas.  In  the 
first  place,  the  elastic  force  of  such  a  mass  would  cause  it 
to  expand  bej'ond  all  limits  when  placed  in  a  position  where 
there  is  absolutely  no  pressure  to  confine  it,  as  in  tlie  celestial 
spaces.  Again,  a  gas  cannot,  so  far  as  experiment  has  ever 
gone,  shine  by  its  own  light  until  it  is  heated  to  a  high  tem- 
perature, far  above  any  that  can  possibly  exist  at  distances 
from  the  sun  so  great  as  those  at  which  comets  have  been 
situated  wlien  under  examination  with  the  spectroscope.  Fi- 
nally, in  tlie  event  of  a  purely  gaseous  comet  being  broken 
up  and  dissipated,  as  in  the  case  of  Biela's  comets  it  is  hardly 
possible  to  suppose  that  it  would  separate  into  innumerable 
widely  detached  pieces,  as  this  comet  did.  The  gaseous  the- 
ory can,  therefore,  not  be  regarded  as  satisfactory.  It  may  be 
that  comets  will  hereafter  be  found  to  consist  of  some  combi- 
nation of  solid  and  gaseous  matter,  the  exact  nature  of  which 
is  not  yet  determined ;  or  it  may  be  that  this  matter  is  of  a 
nature  or  in  a  form  wholly  unlike  anything  that  we  are  ac- 
quainted with  or  can  produce  here  on  the  earth.     As  the  case 


TE3  PHYSICAL   CONSTITUTION  OF  COMETS.  413 

now  stands,  we  must  regard  the  spectrnm  of  a  comet  as  some- 
tiling  not  yet  satisfactorily  accounted  for. 

When  we  turn  from  telescopic  comets  to  those  brilliant 
ones  which  exhibit  a  nucleus  and  a  tail,  we  can  trace  certain 
operations  which  are  not  seen  in  the  case  of  the  others.  What 
the  nucleus  is — whether  it  is  a  solid  body  several  hundred  miles 
in  diameter,  or  a  dense  mass  of  the  same  materials  which  com- 
pose a  telescopic  comet — we  are  quite  unable  to  say.  But 
there  can  hardly  be  any  reasonable  doubt  that  it  is  composed 
of  some  substance  which  is  vaporized  by  the  heat  of  the  solar 
rays!  The  head  of  such  a  comet,  when  carefully  examined 
with  tlie  telescope,  is  found  to  be  composed  of  successive  en- 
velopes or  layers  of  vapor ;  and  when  these  envelopes  are 
watched  from  night  to  night,  they  are  found  to  be  gradually 
rising  upwards,  growing  fainter  and  more  indistinct  in  out- 
line as  they  attain  a  greater  elevation,  until  they  are  lost  in 
the  outlying  parts  of  the  coma.  These  rising  masses  form  the 
fan-shaped  appendage  described  in  a  preceding  section. 

The  strongest  proof  that  some  evaporating  process  is  going 
on  from  the  nucleus  of  the  comet  is  afforded  by  the  move- 
ments of  the  tail.  It  has  long  been  evident  that  the  tail  could 
not  be  an  appendage  which  the  comet  carried  along  with  it, 
and  this  for  two  reasons:  first,  it  is  impossible  that  there  could 
be  any  cohesion  in  a  mass  of  matter  of  such  tenuity  that  the 
smallest  stars  could  be  seen  through  a  million  of  miles  of  it, 
and  which,  besides,  constantly  changes  its  form ;  secondly,  as 
a  comet  flies  around  the  sun  in  its  immediate  neighborhood, 
the  tail  appears  to  move  from  one  side  of  the  sun  to  another 
with  a  rapidity  which  would  tear  it  to  pieces,  and  send  the 
separate  parts  flying  off  in  hyperbolic  orbits,  if  the  movement 
were  real.  The  inevitable  conclusion  is  that  the  tail  is  not  a 
fixed  appendage  of  the  comet,  which  the  latter  carries  with  it, 
but  a  stream  of  vapor  rising  from  it,  like  smoke  from  a  chim- 
ney. As  the  line  of  smoke  which  we  now  see  coming  from 
the  chimney  is  not  the  saine  which  we  saw  a  minute  ago,  be- 
cause the  latter  has  been  blown  away  and  dissipated,  so  we  do 
not  see  the  same  tail  of  a  comet  all  the  time,  because  tlie  mat- 


414  THE  SOLAR  SYSTEM. 

ter  which  makes  np  the  tail  is  constantly  streaming  outwards, 
and  constantly  being  replaced  by  new  vapor  rising  from  the 
nucleus.  The  evaporation  is,  no  doubt,  due  to  the  heat  of  the 
sun,  for  there  can  be  no  evaporation  without  heat,  and  the 
tails  of  comets  increase  enormously  as  they  approach  the  sun. 
Altogether,  a  good  idea  of  the  operations  going  on  in  a  comet 
will  be  obtained  if  we  conceive  the  nucleus  to  be  composed  of 
water  or  other  volatile  fluid  which  is  boiling  away  under  the 
heat  of  the  sun,  while  the  tail  is  a  column  of  steam  rising 
from  it. 

We  now  meet  a  question  to  which  science  has  not  yet  been 
able  to  return  a  conclusive  answer.  Why  does  this  mass  of 
vapor  always  fly  away  from  the  sun  ?  That  the  matter  of  the 
comet  should  be  vaporized  by  the  sun's  rays,  and  that  the  nu- 
cleus should  thus  be  enveloped  in  a  cloud  of  vapor,  is  perfect- 
ly natural,  and  entirely  in  accord  with  the  properties  of  mat- 
ter which  we  observe  around  us.  But,  according  to  all  known 
laws  of  matter,  this  vapor  should  remain  around  the  head,  ex- 
cept that  the  outer  portions  would  be  gradually  detached  and 
thrown  off  into  separate  orbits.  There  is  no  known  tendency 
of  vapor,  as  seen  on  the  earth,  to  recede  from  the  sun,  and  no 
known  reason  why  it  should  so  recede  in  the  celestial  spaces. 
Various  theories  have  been  propounded  to  account  for  it ;  but 
as  they  do  not  rest  on  causes  which  we  have  verified  in  other 
cases,  they  must  be  regarded  as  purely  hypothetical. 

The  first  of  these  explanations,  in  the  order  of  time,  is  due 
to  Kepler,  who  conceived  the  matter  of  the  tail  to  be  driven 
off  by  the  impulsion  of  the  solar  rays,  which  thus  bleached 
the  comet  as  they  bleacli  cloths  here.  If  light  were  an  emis- 
sion of  material  particles,  as  Xewton  supposed  it  to  be,  this 
view  would  have  some  plausibility.  But  light  is  now  con- 
ceived to  consist  of  vibrations  in  an  ethereal  medium  ;  and 
tliere  is  no  known  way  in  which  they  could  exert  any  propel- 
ling force  on  matter.  Two  or  three  years  ago,  it  was  for 
a  while  supposed  that  the  ''  radiometer  "  of  Mr.  Crookes  might 
really  indicate  sucli  an  action  of  tlie  solar  rays  upon  matter 
in  a  vacuum,  but  it  is  now  found  that  the  action  exhibited  m 


THE  PHYSICAL   CONSTITUTION  OF  COMETS.  415 

really  due  to  a  minute  quantity  of  air  left  in  the  instrument. 
Had  Mr.  Crookes  shown  tliat  the  motion  of  his  radiometer 
was  really  due  to  the  impulsion  of  the  solar  rays,  we  might 
be  led  to  the  remarkable  conclusion  that  Kepler's  theory, 
though  rejected  for  more  than  two  centuries,  was,  after  all, 
quite  near  the  truth. 

Sir  Isaac  Newton,  being  the  author  of  the  emission  theory 
of  light,  could  not  dispute  the  possibility  of  Kepler's  views 
being  correct,  but  nevertheless  gave  the  preference  to  anoth- 
er hypothesis.  He  conceived  the  celestial  spaces  to  be  filled 
with  a  veiy  rare  medium,  through  which  the  sun's  rays  passed 
without  heating  it,  as  they  pass  through  cold  air.  But  the 
comet  being  warmed  up  by  the  rays,  the  medium  surrounding 
it  is  warmed  up  by  contact,  and  thus  a  warm  current  is  sent 
out  from  the  comet,  just  as  a  current  of  warm  air  rises  from 
a  heated  body  on  the  surface  of  the  earth.  This  current  car- 
ries the  vapor  of  the  comet  with  it,  and  thus  gives  rise  to  the 
tail  in  the  same  way  that  the  current  of  warm  air  rising  from 
a  chimney  carries  up  a  column  of  smoke.  It  has  long  been 
established  that  there  is  no  medium  in  the  planetary  spaces 
in  which  such  an  effect  as  this  is  possible :  Newton's  theory 
is,  therefore,  no  longer  considered. 

In  recent  times,  Zollner  has  endeavored  to  account  for  the 
tail  of  the  comet  by  an  electrical  action  between  the  sun  and 
the  vapor  rising  from  the  nucleus  of  the  comet.  The  various 
papers  in  which  he  has  elaborated  his  views  of  the  constitu- 
tion of  comets  are  marked  by  profound  research  ;  and  we 
must  regard  his  theories  as  those  which,  on  the  wliole,  most 
completely  explain  all  the  phenomena.  But  they  still  lack 
the  one  thing  needful  to  secure  their  reception :  there  is  no 
evidence  that  the  sun  acts  as  an  electrified  body ;  and  until 
such  evidence  is  adduced  by  experiment,  or  by  observation  on 
other  bodies  than  comets,  the  electric  theory  of  the  comet's 
tail  can  only  be  regarded  as  a  more  or  less  probable  hypothe- 
sis. Indeed,  some  physicists  claim  that  any  such  electric  ac- 
tion in  the  planetary  spaces  is  impossible.  Before  any  theory 
can  be  definitely  settled  upon,  accurate  observations  must  be 
T  28 


416  THE  SO  LAB  SYSTEM. 

made  npon  the  tails  of  comets  with  a  view  of  learning  the 
law  according  to  which  the  vapor  is  repelled  from  the  sun. 
Such  observations  were  made  by  Bessel  on  Halley's  comet  in 
1835,  and  by  various  observers  on  the  great  comet  of  1858. 
The  former  M-ere  investigated  by  Bessel  himself,  and  the  lat- 
ter by  several  mathematicians,  among  them  Professor  Peirce, 
whose  results  are  found  in  a  paper  communicated  to  the 
American  Academy  in  1859.  Pie  found  the  repulsive  force 
of  the  sun  upon  the  particles  which  form  the  front  edge  of 
the  tail  to  be  1^  times  its  attractive  force  upon  ordinary 
bodies  at  the  same  distance.  It  seemed  constantly  to  diminish 
as  the  back  edge  of  the  tail  was  approached ;  but,  owing  to 
the  poor  definition  of  this  edge,  and  the  uncertainty  whether  it 
was  composed  of  a  continuous  stream  of  particles,  the  amount 
of  the  diminution  could  not  be  accurately  fixed.  The  suc- 
cessive envelopes  were  found  to  ascend  uniformly  towards 
the  sun  at  the  rate  of  about  thirty-five  miles  an  hour.  Bond, 
from  a  careful  examination  of  all  the  observations,  was  led  to 
the  result  that  the  rate  of  ascent  diminished  as  the  height 
became  greater. 

The  question  is  frequently  asked.  What  would  be  the  effect 
if  a  comet  should  strike  the  earth?  A  siifiicient  answer  is  that 
the  event  is  too  far  beyond  reasonable  probability  to  give  any 
interest  to  the  subject. 

§  9.  The  Zodiacal  Light. 

This  object  consists  of  a  very  soft,  faint  column  of  light, 
which  may  be  seen  rising  from  the  western  horizon  after  twi- 
light on  any  clear  winter  or  spring  evening :  it  may  also  be 
seen  rising  from  the  eastern  horizon  just  before  daybreak  in 
the  summer  or  autumn.  It  really  extends  out  on  each  side 
of  the  sun,  and  lies  nearly  in  the  plane  of  the  ecliptic.  The 
reason  it  cannot  be  well  seen  in  the  summer  and  autumn 
evenings  is,  that  in  our  latitudes  the  course  of  the  ecliptic  in 
the  south-west  is,  during  those  seasons,  so  near  the  horizon  that 
the  light  in  question  is  extinguished  by  the  great  thickness  of 
atmosphere  through  which  it  has  to  pass,     Xear  the  equator. 


THE  ZODIACAL  LIGHT.  417 

where  the  ecliptic  always  rises  high  above  the  horizon,  the 
lig-lit  can  be  seen  about  equally  well  all  the  year  round.  It 
grows  fainter  the  farther  it  is  from  the  sun,  and  can  gener- 
ally be  traced  to  about  90°  from  that  luminary,  when  it  grad- 
ually fades  away.  But  in  a  very  clear  atmosphere,  between 
the  tropics,  it  has  been  traced  all  the  way  across  the  heavens, 
from  east  to  west,  thus  forming  a  complete  ring. 

Such  is  the  zodiacal  light  as  it  appears  to  the  eye.  Put- 
ting its  appearances  all  together,  we  may  see  that  it  is  due  to 
a  lens -shaped  appendage  of  some  sort  surrounding  the  sun, 
and  extending  out  a  little  beyond  the  ej|rth's  orbit.  It  lies 
very  nearly  in  the  plane  of  the  ecliptic,  but  its  exact  position 
is  difficult  to  determine,  not  only  owing  to  its  indistinct  out- 
line, but  because  in  northern  latitudes  the  southern  edge  will 
be  dimmed  by  the  greater  thickness  of  atmosphere  through 
which  it  is  seen,  and  thus  the  liglit  will  look  farther  north 
than  it  really  is.  The  nature  of  the  substance  from  which 
this  light  emanates  is  entirely  unknown.  Its  spectrum  has 
been  examined  by  several  observers,  some  of  whom  have  re- 
ported it  as  consisting  of  a  single  yellow  line,  and  therefore 
arising  from  an  incandescent  gas.  This  would  indicate  a  len- 
ticular-shaped atmosphere  of  inconceivable  rarity  surrounding 
the  sun,  and  extending  out  near  the  plane  of  the  ecliptic  be- 
yond the  orbit  of  the  earth.  But  Professor  Wright,  of  Yale 
College,  who  has  made  the  most  careful  observations  of  this 
spectrum,  finds  it  to  be  continuous.  For  several  reasons,  too 
minute  to  enter  into  now,  this  observation  seems  to  the  writer 
more  likely  to  be  correct.  Accepting  it,  we  should  be  led  to 
the  conclusion  that  the  phenomenon  in  question  is  due  to  re- 
flected sunlight,  probably  from  an  immense  cloud  of  meteor- 
oids  filling  up  the  space  between  the  earth  and  sun.  But  fur 
tlier  researches  must  be  made  before  a  conclusive  result  can 
be  reached. 

One  important  question  respecting  the  zodiacal  light  is  sug- 
gested by  the  motion  of  the  perihelion  of  Mercury  already 
described.  This  motion  seems  to  prove  one  of  two  things: 
either  that  the  sun's  gravitation  does  not  strictly  follow  the 


418  THE   SOLAR  SYSTEM. 

law  of  the  invei-se  square  of  the  distance,  or  tliat  there  is  a 
mass  of  matter  of  some  kind  between  tlie  earth  and  the  smi. 
Can  this  matter  be  that  from  which  the  "zodiacal  light"  is 
reflected  ?  It  is  impossible  to  make  a  positive  answer  to  this 
question. 

Another  mysterious  phenomenon  associated  with  the  zodi- 
acal light  is  known  by  its  German  appellation,  the  Gegen- 
schein.  It  is  said  that  in  that  point  of  the  heavens  directly 
opposite  the  sun  there  is  an  elliptical  patch  of  light,  a  few  de- 
grees in  extent,  of  such  extreme  faintness  that  it  can  be  seen 
only  by  the  most  scyisitive  eyes,  under  the  best  conditions,  and 
through  the  clearest  atmosphere.  This  phenomenon  seems  so 
difficult  to  account  for  tliat  its  existence  is  sometimes  doubted; 
yet  the  testimony  in  its  favor  is  difficult  to  set  aside.* 

*  The  latest  observations  upon  this  phenomenon  have  been  made  near  Phila- 
delphia by  Mr.  Lewis,  and  are  found  in  the  American  Journal  of  Science  and 
Arts  for  1879. 


PART  IV.— THE  STELLAR  UNIVERSE. 


INTKODUCTORY  EEMAEKS. 

Hitherto  our  attention  has  been  principally  occupied  with 
the  bodies  which  surround  our  sun  and  make  up  the  solar  sys- 
tem. Notwithstanding  the  immense  distances  at  which  these 
bodies  are  found,  we  may  regard  tliem,  in  comparison  with  the 
fixed  stars,  as  an  isolated  family  immediately  surrounding  us, 
since  a  sphere  as  large  as  the  whole  solar  system  would  only 
appear  as  a  point  to  the  vision  if  viewed  from  the  nearest 
star.  The  space  which  separates  the  orbit  of  Neptune  from 
the  fixed  stars  and  the  fixed  stars  from  each  other  is,  so  far  as 
we  can  learn,  entirely  void  of  all  visible  matter,  except  occa- 
sional waste  nebulous  fragments  of  a  meteoric  or  cometary 
nature  which  are  now  and  then  drawn  in  by  the  attraction  of 
our  sun. 

The  widest  question  which  the  study  of  the  stars  presents 
to  us  may  be  approached  in  this  way :  "We  have  seen,  in  our 
system  of  sun,  planets,  and  satellites,  a  very  orderly  and 
beautiful  structure,  every  body  being  kept  in  its  own  orbit 
through  endless  revolutions  by  a  constant  balancing  of  gravi- 
tating and  centrifugal  forces.  Do  the  millions  of  suns  and 
clusters  scattered  through  space,  and  brought  into  view  by  the 
telescope,  constitute  a  greater  system  of  equally  orderly  struct- 
ure %  and,  if  so,  what  is  that  structure  ?  If  we  measure  the 
importance  of  a  question,  not  by  its  relations  to  our  interests 
and  our  welfare,  but  by  the  intrinsic  greatness  of  the  subject 
to  which  it  relates,  tlien  we  must  regard  this  question  as  one 
of  the  noblest  with  which  the  human  mind  has  ever  been 


420  TBE  STELLAB   UNIVERSE. 

occupied.  In  piercing  the  mystery  of  the  solar  system,  and 
showiuo:  that  the  earth  on  Avhich  we  dwell  was  only  one  of 
the  smaller  of  eight  planets  which  move  around  the  sun,  we 
made  a  great  step  in  the  way  of  enlarging  our  ideas  of  the 
immensity  of  creation  and  of  the  comparative  insignificance 
of  our  sublunary  interests.  But  when,  on  extending  our  view, 
we  find  our  sun  to  be  but  one  out  of  unnumbered  millions,  we 
see  that  our  whole  system  is  but  an  insignificant  part  of  crea- 
tion, and  tiiat  we  have  an  immensely  greater  fabric  to  study. 
"Wlien  we  have  bound  all  the  stars,  nebulee,  and  clusters  which 
our  telescopes  reveal  into  a  single  system,  and  shown  in  what 
manner  each  stands  related  to  all  the  others,  we  shall  have 
solved  the  problem  of  the  material  univei-se,  considered,  not  in 
its  details,  but  in  its  widest  scope. 

From  the  time  that  Copernicus  showed  the  stai-s  to  be  self- 
luminous  bodies,  situated  far  outside  of  our  solar  system,  the 
question  thus  presented  has  occupied  the  attention  of  the  phil- 
osophical class  of  astronomers.  The  original  view,  which  has 
been  the  starting-point  of  all  speculation  on  the  subject,  we 
have  described  in  the  Introduction  as  that  of  a  spherical  uni- 
verse. The  apparent  sphericity  of  the  vault  of  heaven,  the 
uniformity  of  the  diurnal  revolution,  and  the  invariability  of 
the  relative  positions  of  the  stars,  all  combined  to  strengthen 
the  idea  that  the  latter  were  set  on  the  interior  surface  of  a 
Liollow  sphere,  having  the  earth  or  the  sun  in  its  centre.  This 
sphere  constituted  the  firmament  of  the  ancients,  outside  of 
which  was  situated  the  empyrean,  or  kingdom  of  fire.  Coper- 
nicus made  no  advance  whatever  on  tliis  idea.  Galileo  and 
Kepler  seem  to  have  made  the  first  real  advance — the  former 
by  resolving  the  Milky  Way  into  stars  with  his  telescope,  the 
latter  by  suggesting  that  our  sun  might  be  simply  one  of  nu- 
merous stars  scattered  through  space,  looking  so  bright  only 
on  account  of  our  proximity  to  it.  In  the  problem  of  the 
stellar  system  this  conception  held  the  same  important  place 
which  that  of  the  earth  as  a  planet  did  in  the  problem  of  the 
solar  system.  But  Kepler  was  less  fortunate  than  Copernicus 
in  that  he  failed  to  commend  his  idea,  even  to  his  own  judg- 


INTBODUCTOBY  BEMABKS.  421 

ment.  It  was  by  affording  a  starting-point  for  the  researches 
of  Kant  and  Ilerschel  that  Kepler's  suggestion  really  bore 
frnit. 

Notwithstanding  the  amount  of  careful  research  which 
Herschel  and  his  successors  have  devoted  to  it,  we  are  still 
very  far  from  having  reached  even  an  approximate  solution 
of  the  problem  of  which  we  speak.  In  whatever  direction  we 
pursue  it,  we  soon  find  ourselves  brought  face  to  face  with  the 
infinite  in  space  and  time.  Especially  is  this  the  case  when 
we  seek  to  know,  not  simply  what  the  universe  is  to-day,  but 
what  causes  are  modifying  it  from  age  to  age.  All  the  knowl- 
edge that  man  has  yet  gathered  is  then  found  to  amount  to 
nothing  but  some  faint  glimmers  of  light  shining  here  and 
there  through  the  seemingly  boundless  darkness.  The  glim- 
mer is  a  little  brighter  for  each  successive  generation,  but 
many  centuries  must  elapse  before  we  can  do  much  more 
than  tell  how  the  nearer  stars  are  situated  in  space.  Indeed, 
we  see  as  yet  but  little  hope  that  an  inhabitant  of  this  planet 
will  ever,  from  his  own  observations  and  those  of  his  prede- 
cessors, be  able  to  completely  penetrate  the  mystery  in  which 
the  structure  and  destiny  of  the  cosmos  are  now  enshrouded. 
However  this  may  be  in  tlie  future,  all  we  can  do  at  present 
is  to  form  more  or  less  probable  conjectures,  founded  on  all 
we  know  of  the  general  character  of  natural  law.  In  a  strictly 
scientific  treatise,  such  conjectures  would  find  no  place  ;  and 
if  we  had  to  grope  in  absolute  darkness,  they  would  be  en- 
tirely inappropriate  in  any  but  a  poetical  or  religious  produc- 
tion. But  the  subject  is  too  fascinating  to  permit  us  to  neg- 
lect the  faintest  light  by  the  aid  of  M'liich  we  may  penetrate 
the  mystery;  we  shall  therefore  briefly  set  forth  both  what 
men  of  the  past  have  thought  on  the  subject,  what  the  science 
of  to  day  enables  us  to  assert  with  some  degree  of  probability, 
and  what  knowledge  it  wholly  denies  us.  To  proceed  in  sci- 
entific order,  we  must  commence  by  laying  a  wide  foundation 
of  facts.  Our  first  step  will  therefore  be  to  describe  the  heav- 
ens as  they  appear  to  the  naked  eye,  and  as  they  are  seen  in 
the  telescope. 


422  THE  STELLAE   VXIVEESE. 


CHAPTER  I. 

THE  STARS  AS  THEY  AEE  SEEN. 

§  1.  Number  and  Orders  of  Stars  and  Kebulce. 

The  total  number  of  stars  in  the  celestial  sphere  visible 
with  the  average  naked  eye  may  be  estimated,  in  round  num- 
bers, as  5000.  The  number  varies  so  much  with  the  perfec- 
tion and  training  of  the  eye,  and  with  the  atmospheric  condi- 
tions, that  it  cannot  be  stated  very  definitely.  When  the  tele- 
scope is  pointed  at  the  heavens,  it  is  found  that  for  every  star 
visible  to  the  naked  eye  there  are  hundreds,  or  even  thousands, 
too  minute  to  be  seen  without  artificial  aid.  From  the  counts 
of  stars  made  by  Herschel,  Struve  has  estimated  that  the  total 
number  of  stars  visible  with  HerschePs  twenty-foot  telescope 
was  about  20,000,000.  The  great  telescopes  of  modern  times 
woiild,  no  doubt,  show  a  yet  larger  number ;  but  a  reliable 
estimate  has  not  been  made.  The  number  is  probably  some- 
where between  30,000,000  and  50,000,000. 

At  a  very  early  age,  the  stars  were  classified  according  to 
their  apparent  brightness  or  magnitude.  Tlie  fifteen  brightest 
ones  were  said  to  be  of  the  first  magnitude;  the  fifty  next  in 
order  were  termed  of  the  second  magnitude,  and  so  on  to  the 
sixth,  which  comprised  the  faintest  stai*s  visible  to  the  naked 
eye.  The  number  of  stars  of  each  order  of  magnitude  be- 
tween the  north  pole  and  the  circle  35°  south  of  the  equator 
is  about  as  follows : 

Of  magnitude  1  there  are  about 14  stars. 

"     2      "     48  " 

"     3      "     152  " 

"     4      "     313  " 

"     5      "     854  " 

"     6      "     2010  " 

Total  visible  to  naked  eve 3391     " 


NUMBER  AND   OBDEES  OF  STABS  AND  NEBULA.      423 

This  limit  includes  all  the  stars  which,  in  the  Middle  States, 
culminate  at  a  greater  altitude  than  15°.  The  number  of  the 
sixth  magnitude  which  can  be  seen  depends  very  much  upon 
the  eye  of  the  observer  and  the  state  of  the  sky.  The  forego- 
ing list  includes  all  that  can  be  seen  by  an  ordinary  good  eye 
in  a  clear  sky  when  there  is  no  moonlight ;  but  the  German 
astronomer  Heis,  from  whom  these  numbers  are  taken,  gives  a 
list  of  1964  more  which  he  believes  he  can  see  without  a  glass. 

The  system  of  expressing  the  brightness  of  the  stars  by  a 
series  of  numbers  is  continued  to  the  telescopic  stars.  The 
smallest  star  visible  with  a  six-inch  telescope  under  ordinary 
circumstances  is  conunonly  rated  as  of  the  thirteenth  magni- 
tude. On  the  same  scale,  the  smallest  stars  visible  with  the 
largest  telescopes  of  the  world  would  be  of  about  the  six- 
teenth magnitude,  but  no  exact  scale  for  these  very  faint  stars 
has  been  arranged. 

Measures  of  the  relative  brilliancy  of  the  stars  indicate 
that,  as  we  descend  in  the  scale  of  magnitude,  the  quantity 
of  light  emitted  diminishes  in  a  geometrical  ratio,  the  stars 
of  each  order  being,  in  general,  between  two-fifths  and  one- 
third  as  bright  as  those  of  the  order  next  above  them.  Tliis 
order  of  diminution  is  not,  however,  exact,  because  the  arrange- 
ment of  magnitudes  has  been  made  by  mere  estimation  of  in- 
dividual observers  who  may  have  hit  on  different  and  varying 
ratios ;  but  it  is  a  sufficient  approach  to  the  truth  for  common 
purposes.  From  the  second  to  the  fifth  magnitude  the  dimi- 
nution is  probably  one -third  in  each  magnitude,  after  that 
about  two-fifths.  Supposing  the  ratio  two-fifths  to  be  exact, 
we  find  that  it  would  take  about 

2k  stars  of  the  second  magnitude  to  make  one  of  the  first. 


6 

third 

16 

fourth 

40 

fifth 

100 

sixth 

10,000 

eleventh 

1,000,000 

sixteenth 

The  number  of  stars  of  the  several  scales  of  magnitude 
vai'y  in  a  ratio  not  far  different  from  the  inverse  of  that  of 


424  THE  STELLAR   UNIVERSE. 

their  brightness,  the  ratio  being  a  little  greater  in  the  ease  of 
the  higher  magnitudes,  and  probably  a  little  less  in  the  case 
of  the  lower  ones.  Thus,  we  see  that  there  are  about  three 
times  as  many  stars  of  the  second  magnitude  as  of  the  first, 
three  times  as  many  of  the  third  as  of  the  second,  and  after 
that  something  less  than  three  times  as  many  of  each  magni- 
tude as  of  the  magnitude  next  above.  Comparing  this  with 
the  table  of  relative  brightness  just  given,  we  may  conclude 
that  if  all  the  stars  of  each  magnitude  were  condensed  into  a 
single  one,  the  brightness  of  tlie  combined  stars  thus  formed 
would  not  vary  extravagantly  from  one  to  another  until  we 
had  passed  beyond  the  ninth  or  tenth  magnitude.  But  it  is 
certain  that  the  brightness  would  ultimately  diminish,  because 
otherwise  there  would  be  no  limit  to  the  total  amount  of  light 
given  by  the  stars,  and  the  whole  heavens  would  shine  like 
the  sun. 

The  i-eader  will,  of  course,  understand  that  this  arrange- 
ment by  magnitude  is  purely  artificial.  Really  the  stars  are 
of  every  order  of  brightness,  varying  by  gradations  which  are 
entirely  insensible,  so  that  it  is  impossible  to  distinguish  be- 
tween the  brightest  star  of  one  magnitude  and  the  faintest  of 
the  magnitude  next  above  it.  Hence,  those  astronomers  who 
wish  to  express  magnitudes  with  the  greatest  exactness,  divide 
them  into  thirds  or  even  tenths ;  so  that,  for  instance,  stars  be- 
tween the  sixth  and  seventh  magnitudes  are  called  6.1,  6.2, 
6.3,  and  so  ou  to  6.9,  according  to  their  brilliancy.  Various 
attempts  have  been  made  to  place  the  problem  of  the  relative 
amounts  of  light  emitted  by  the  stars  upon  a  more  exact  basis 
than  this  old  one  of  magnitudes,  but  this  is  a  very  difiicult 
thing  to  do,  because  there  is  no  way  of  measuring  light  except 
by  estimation  with  the  eye.  In  order  to  measure  the  relative 
intensity  of  two  lights,  it  is  necessary  to  have  some  instrument 
by  which  the  intensity  of  one  or  both  the  lights  may  be  varied 
until  the  two  appear  to  be  equal.  Instruments  for  this  pur- 
pose are  known  as  photometers,  and  are  of  various  construc- 
tions. For  comparing  the  light  of  different  stars,  the  photom- 
eter most  used  at  the  present  time  is  that  of  Zollner.     Bv 


NUMBER  AND   ORDERS  OF  STARS  AND  NEBULxE.      425 

this  instrument  the  h'ght  of  the  stars,  as  seen  through  a  small 
telescope,  is  compared  both  in  color  and  intensity  M'ith  that  of 
an  artificial  star,  the  liglit  of  which  can  be  varied  at  pleasure. 
A  complete  set  of  measures  with  this  instrument,  including 
most  of  the  brighter  stars,  is  one  of  the  wants  of  astronomy 
which  we  may  soon  hope  to  see  supplied.  The  most  extended 
recent  series  of  photometric  estimates  with  which  the  writer 
is  acquainted  is  that  of  Professor  Seidel,  of  Munich,  which  in- 
cludes 209  stars,  tlie  smallest  of  which  are  of  the  lifth  magni- 
tude. An  interesting  result  of  these  estimates  is  that  Siriua 
gives  us  four  times  as  much  light  as  any  other  star  visible  in 
our  latitude. 

Catalogues  of  Stars. — In  nearly  every  age  in  which  astron- 
omy has  flourished  catalogues  of  stars  have  been  made,  giving 
their  positions  in  the  heavens,  and  the  magnitude  of  each. 
The  earliest  catalogue  which  has  come  to  us  is  found  in  the 
"Almagest"  of  Ptolemy,  and  is  supposed  to  be  that  of  Hippar- 
chus,  wlio  flourished  150  years  before  the  Christian  era.  It 
is  said,  but  not  on  the  best  authority,  that  he  constructed  it  in 
order  that  future  generations  might  And  whether  any  change 
had  in  the  mean  time  taken  place  in  the  starry  heavens.  An 
examination  of  the  catalogue  shows  that  the  constellations  pre- 
sented much  the  same  aspect  two  thousand  years  ago  that  they 
do  now.  There  are  two  or  three  stars  of  his  catalogue  which 
cannot  now  be  certainly  identified  ;  but  it  is  probable  that  the 
difliculty  arises  from  the  imperfection  of  the  catalogue,  and 
from  the  errors  which  may  have  crept  into  the  nnmerous 
transcriptions  of  it  during  the  sixteen  centuries  which  elapsed 
before  the  art  of  printing  was  discovered.  The  catalogue  of 
Ilipparchus  contains  only  about  lOSO  stars,  so  that  he  could 
not  have  given  all  that  he  was  able  to  see.  He  probably  omit- 
ted many  stars  of  the  smaller  magnitudes.  The  actual  num- 
ber given  in  the  "Almagest"  is  still  less,  being  only  1030. 

The  next  catalogue  in  the  order  of  time  is  that  of  Ulugh 
Beigh,  a  son  of  the  Tartar  monarch  Tamerlane,  which  dates 
from  the  fifteenth  century.  For  the  most  part,  the  stars  are 
the  same  as  in  the  catalogue  of  Ptolemy,  only  the  places  were 


426  TEE  STELLAS   UXIVEBSE. 

redetermined  from  the  observations  at  Samarcand.  It  con- 
tains  1019  stars,  eleven  less  than  Ptolemy  gives.  Tjcho  Brahe, 
having  made  so  great  an  improvement  in  the  art  of  observa- 
tion, very  naturally  recatalogued  tlie  stars,  determining  their 
positions  with  yet  greater  accuracy  than  his  predecessors.  His 
catalogue  is  the  third  and  last  important  one  formed  before 
the  invention  of  the  telescope.     It  contains  1005  stars. 

Our  modern  catalogues  may  be  divided  into  two  classes: 
those  in  which  the  position  of  each  star  in  the  celestial  sphere 
(right  ascension  and  declination)  is  given  with  all  attainable 
precision,  and  those  in  which  it  is  only  given  approximately, 
so  as  to  identify  the  star,  or  distinguish  it  from  others  in  its 
neighborhood.  The  catalogues  of  the  former  class  are  very 
numerous,  but  the  more  accurate  ones  are  necessarily  incom- 
plete, owing  to  the  great  labor  of  making  the  most  exact  de- 
termination of  the  position  of  a  star.  There  are,  perhaps, 
between  ten  or  twenty  thousand  stars  the  positions  of  M'hich 
are  catalogued  with  astronomical  precision,  and  a  hundred 
thousand  more  in  which,  though  entire  precision  is  aimed  at, 
it  is  not  attained.  Of  the  merely  approximate  catalogues,  the 
greatest  one  is  the  '*'  Sternverzeichniss  "  of  Argelander,  which 
enumerates  all  the  stars  down  to  the  ninth  magnitude  between 
the  pole  and  two  degrees  south  of  the  equator.  The  work 
fills  three  thin  quarto  volumes,  and  the  entire  number  of  stars 
catalogued  in  it  exceeds  three  hundred  thousand.  This  "  star 
census"  is  being  continued  to  the  south  pole  at  the  observa- 
tory of  Cordoba,  South  America,  by  Dr.  Gould.  Of  the  mill- 
ions of  stars  of  the  tenth  magnitude  and  upwards,  hardly  one 
in  a  thousand  is.  or  can  be,  individually  known  or  catalogued. 
Except  as  one  or  another  may  exhibit  some  remarkable  pecu- 
liarity, they  must  pass  unnoticed  in  the  crowd. 

Division  into  Constellations. — A  single  glance  at  the  heavens 
shows  that  the  stars  are  not  equally  scattered  over  the  sky,  but 
that  great  numbers  of  them,  especially  of  the  brighter  ones, 
are  collected  into  extremely  irregular  groups,  known  as  con- 
stellations. At  a  very  early  age  the  heavens  were  represented 
as  painted  over  with  figures  of  men  and  animals,  so  arranged 


NUMBER  AND   OBDEBS   OF  STABS  AND  NEBULJE.       427 

as  to  include  the  principal  stars  of  each  constellation.  There 
is  no  historic  record  of  the  time  when  this  was  done,  nor  of  tlie 
principles  by  which  those  who  did  it  carried  out  tjieir  work ; 
l3nt  many  of  the  names  indicate  that  it  was  during  the  heroic 
age.  Some  have  sought  to  connect  it  with  the  Argonantic  ex- 
pedition, from  the  fact  that  several  heroes  of  that  expedition 
were  among  those  thus  translated  to  the  heavens ;  but  this  is 
little  more  than  conjecture.  So  little  pains  was  taken  to  fit 
the  figures  to  the  constellations  that  we  can  hardly  suppose 
them  to  have  all  been  executed  at  one  time,  or  on  any  well- 
defined  plan.  Quite  likely,  in  the  case  of  names  of  heroes, 
the  original  object  was  rather  to  do  honor  to  the  man  than  to 
serve  any  useful  purpose  in  astronomy.  "Whatever  their  ori- 
gin, these  names  have  been  retained  to  the  present  day,  al- 
though the  figures  which  they  originally  represented  no  longer 
serve  any  astronomical  purpose.  The  constellation  Hercules, 
for  instance,  still  exists ;  but  it  no  longer  represents  the  figure 
of  a  man  among  the  stars,  but  a  somewhat  irregular  portion 
of  the  heavens,  including  the  space  in  which  the  ancients 
placed  that  figure.  In  star-maps,  designed  for  school  instruc- 
tion and  for  common  use,  it  is  still  customary  to  give  these 
figures,  but  they  are  not  generally  found  on  maps  designed 
for  the  use  of  astronomers. 

Naming  the  /Stars.- — The  question  how  to  name  the  individ- 
ual stars  in  each  constellation,  so  as  to  readily  distinguish 
them,  luis  always  involved  some  difliculty.  In  the  ancient 
catalogues  they  were  distinguished  by  the  part  of  the  figure 
representing  the  constellation  in  which  they  were  found ;  as, 
the  eye  of  the  Bull,  the  tail  of  the  Great  Bear,  the  right  shoul- 
der of  Orion,  and  so  on.  The  Arabs  adopted  the  plan  of  giv- 
ing special  names  to  each  of  the  brighter  stars,  or  adopting 
such  names  from  the  Greeks.  Thus,  we  have  the  well-known 
stars  Sirius,  Arcturus,  Procyon,  Aldebaran,  and  so  on.  Most 
of  these  names  have  dropped  entirely  out  of  astronomical  use, 
though  still  found  on  some  school  maps  of  the  stars.  The 
system  now  most  in  use  for  the  brighter  stars  was  desiirncd  by 
Bayer,  of  Augsburg,  Germany,  about  1610.     He  published  a. 


428  THE  STELLAR   UNIVERSE. 

Bet  of  star-maps,  in  which  the  individual  stars  of  each  constel- 
lation were  designated  by  the  letters  of  the  Greek  alphabet — ■ 
a,  jS,  y,  etc.  The  first  letters  were  given  to  the  brightest  stars, 
the  next  ones  to  the  next  brightest,  and  so  on.  After  ths 
Greek  letter  is  given  the  Latin  name  of  the  constellation  in 
the  genitive  case.  Thus,  Alpha  (a)  Scorpii,  or  Alpha  of  the 
Scorpion,  is  the  name  of  Antares,  the  brightest  star  in  Scor- 
pius ;  o  Lyrse,  of  the  brightest  star  in  the  Lyre ;  and  so  on. 
We  have  here  a  resemblance  to  our  system  of  naming  men, 
the  Greek  letter  corresponding  to  the  Christian  name,  and  the 
constellation  to  the  surname.  "When  the  Greek  alphabet  was 
exliausted,  without  including  all  the  conspicuous  stars,  the 
Latin  alphabet  was  drawn  upon. 

The  Bayer  system  is  still  applied  to  all  the  stars  named  by 
him.  Most  of  the  other  stars  down  to  the  fifth  magnitude  are 
designated  by  a  system  of  numbers  assigned  by  Flamsteed  in 
his  catalogue.  Yet  other  stai*s  are  distinguished  by  their  num- 
bers in  some  well-known  catalogue.  When  this  method  fails, 
owing  to  the  star  not  being  catalogued,  the  position  in  the 
heavens  must  be  given. 

The  Milky  Tr«y,  or  Galaxy. — To  the  naked  eye  so  much  of 
the  Galaxy  as  can  be  seen  at  one  time  presents  the  appearance 
of  a  white,  cloud-like  arch,  resting  on  two  opposite  points  of 
the  horizon,  and  rising  to  a  greater  or  less  altitude,  according 
to  the  position  of  the  celestial  sphere  relative  to  the  observer. 
Only  half  of  the  entire  arch  can  be  seen  above  the  horizon  at 
once,  the  other  half  being  below  it,  and  directly  opposite  the 
visible  half.  Lideed,  there  is  a  portion  of  it  which  can  never 
be  seen  in  our  latitude,  being  so  near  the  south  pole  that  it 
is  always  below  our  horizon.  If  the  earth  were  removed,  or 
made  transparent,  so  that  we  could  see  the  whole  celestial 
•sphere  at  once,  the  Galaxy  would  appear  as  a  complete  belt 
extending  around  it.  The  telescope  shows  that  the  Galaxy 
arises  from  the  light  of  countless  stars,  too  minute  to  be  sep- 
arately visible  with  the  naked  eye.  We  find,  then,  that  the 
telescopic  stars,  instead  of  being  divided  up  into  a  limited 
number  of  constellations,  are  mostly  condensed  in  the  region 


DESCRIPTION  OF  THE  PRINCIPAL  CONSTELLATIONS.      429 

of  the  Galaxy,  They  are  least  mimerons  in  the  regions  most 
distant  from  the  galactic  belt,  and  grow  thicker  as  we  ap- 
proach it.  The  more  powerful  the  telescope,  the  more  marked 
the  condensation  is.  With  the  naked  eye,  the  condensation  is 
hardly  noticeable,  unless  by  actual  count:  a  very  small  tele- 
scope will  show  a  decided  thickening  of  the  stars  in  and  near 
the  Galaxy ;  while,  if  we  employ  the  most  powerful  telescopes, 
a  large  majority  of  the  stars  they  show  are  found  to  lie  act- 
ually in  the  Galaxy,  In  other  words,  if  we  should  blot  out 
all  the  stars  visible  witli  a  twelve-inch  telescope,  we  should 
find  that  the  greater  part  of  the  remaining  stars  were  in  the 
Galaxy.  The  structure  of  the  universe  which  this  fact  seems 
to  indicate  will  be  explained  in  a  subsequent  section. 

Clusters.  —  Besides  this  e-radual  and  resrular  condensation 
towards  the  galactic  belt,  occasional  condensations  of  stars 
into  clusters  may  be  seen.  Indeed,  some  of  these  clusters  are 
visible  to  the  naked  eye,  sometimes  as  separate  stars,  like  the 
Pleiades,  but  more  commonly  as  milky  patches  of  light,  be- 
cause the  stars  are  too  small  to  be  seen  separately.  The  num- 
ber visible  in  powerful  telescopes  is,  however,  much  greater. 
Sometimes  there  are  hundreds,  or  even  thousands,  of  stars  visi- 
ble in  the  field  of  the  telescope  at  once;  and  sometimes  the 
number  is  so  great,  and  the  individual  stare  so  small,  that  they 
cannot  be  counted  even  in  the  most  powerful  telescopes  ever 
made. 

Nehulit. — Another  class  of  objects  which  are  found  in  the 
celestial  spaces  are  irregular  masses  of  soft,  cloudy  light, 
which  are  hence  termed  nebuliB.  Many  objects  which  look 
like  nebulae  in  small  telescopes  are  found  by  more  powerful 
ones  to  be  really  star  clusters.  But,  as  we  shall  hereafter 
show,  many  of  these  objects  are  not  composed  of  stars  at  all^ 
but  of  immense  masses  of  gaseous  matter. 

§  2.  Description  of  the  Principal  Constellations. 

For  the  benefit  of  the  reader  who  wishes  to  make  himself 
acquainted  with  the  constellations  in  detail,  or  to  identify  any 
bright  star  or  constellation  which  he  may  see,  we  present  a 


430  THE  STELLAR   UNIVERSE. 

brief  description  of  the  principal  objects  which  may  be  seen 
in  the  lieavens  at  different  seasons,  iUnstrated  by  five  maps, 
showinir  the  stars  to  the  fifth  ma^jnitude  inchisive.  Tlie 
reader  wlio  does  not  wish  to  enter  into  these  details  can  pass 
to  the  next  section  withont  any  break  of  the  continuity  of 
thought. 

For  the  purpose  of  learning  the  constellations,  the  star- 
maps  will  be  a  valuable  auxiliary.  It  will  be  better  to  begin 
with  the  northern,  or  circumpolar,  constellations,  because  these 
are  nearly  always  visible  in  our  latitude.  The  first  one  to  be 
looked  for  is  Ursa  Major  (the  Great  Bear,  or  the  Dipper),  from 
which  the  pole  star  can  always  be  found  by  means  of  the 
pointers,  as  shown  in  Fig.  2,  page  10.  Supposing  the  observer 
to  look  for  it  at  nine  o'clock  in  the  evening,  he  will  see  it  in 
various  positions,  depending  on  the  time  of  year,  namely,  in 

April  and  May north  of  the  zenith. 

July  and  August to  the  west  of  north,  the  pointers  lowest. 

October  and  November close  to  the  north  horizon. 

January  and  February to  the  east  of  north,  the  pointers  highest. 

These  successive  positions  are  in  the  same  order  with  those 
which  the  constellation  occupies  in  consequence  of  its  diurnal 
motion  around  the  pole.  The  pointers  are  in  the  body  of  the 
bear,  while  the  row  of  stars  on  the  other  end  of  the  constella- 
tion forms  his  tail. 

Ursa  Minor,  or  the  Little  Dipper,  is  the  constellation  to 
which  the  pole  star  belongs.  It  includes,  besides  the  pole 
star,  another  star  of  the  second  magnitude,  which  lies  nearly 
in  the  direction  of  the  tail  of  Ursa  Major. 

Cassiojma,  or  the  Lady  in  the  Chair,  is  on  the  opposite  side 
of  the  pole  from  Ursa  Major,  at  nearly  the  same  distance. 
The  constellation  can  be  readily  recognized  from  its  three  or 
four  bright  stars,  disposed  in  a  line  broken  into  pieces  at  right 
angles  to  each  other.  In  the  ancient  mj'thology,  Cassiopeia  is 
the  queen  of  Cepheus ;  and  in  the  constellation  she  is  repre- 
sented as  seated  in  a  large  chair  or  throne,  from  which  she  is 
issuing  her  edicts. 

Perseus  is  quite  a  brilliant  constellation,  situated  in  the 


DESCRIPTION  OF  THE  PRINCIPAL  CONSTELLATIONS.     431 

Milky  Way,  east*  of  Cassiopeia,  and  a  little  farther  fr(»m  the 
pole.  It  may  be  recognized  by  a  row  of  conspicuous  stars 
extending  along  the  Milky  Way,  which  passes  directly  through 
this  constellation. 

Other  circumpolar  constellations  are  Cepheus,  the  Camelo- 
pard,  the  Lynx,  the  Dragon  {Draco),  and  the  Lizard  ;  but  they 
do  not  contain  any  stars  so  bright  as  to  attract  especial  atten- 
tion. The  reader  who  wishes  to  learn  them  can  easily  lind 
them  by  comparing  the  star-maps  with  the  heavens. 

Owino;  to  the  annual  motion  of  the  sun  amono;  the  stars,  the 
constellations  which  are  more  distant  from  the  pole  cannot  be 
seen  at  all  times,  but  must  be  looked  for  at  certain  seasons, 
unless  inconvenient  hours  of  the  night  be  chosen.  We  shall 
describe  the  more  remarkable  constellations  as  they  are  seen 
by  an  observer  in  middle  north  latitudes  in  four  different 
positions  of  the  starry  sphere.  The  sphere  takes  all  four  of 
these  positions  every  day,  by  its  diurnal  motion ;  but  some  of 
these  positions  will  occur  in  the  daytime,  and  others  late  at 
night  or  early  in  the  morning. 

First  Position.!  Orion  on  the  Meridian.  —  The  constellations 
south  of  tlie  zenith  are  those  shown  on  Maps  II.  and  III.,  the 
former  being  w^est  of  the  meridian,  the  latter  east.  This  posi- 
tion occurs  on 

December  21st at  midnight. 

Jammry  21st at  10  o'clock  p.m. 

February  20th at  8  o'clock  p.m. 

March  21st at  6  o'clock  p.m. 

And  so  on  through  the  year.  In  this  position,  Cassiopeia  and 
Ursa  Major  are  near  the  same  altitude,  the  former  high  up  in 

*  In  the  celestial  sphere  the  points  of  the  compass  have,  of  necessity,  a  mean- 
ing which  may  seem  different  from  that  \vhic:h  we  attribute  to  them  on  the  earth. 
North  always  means  towards  the  north  pole ;  south,  from  it ;  west,  in  the  direc- 
tion of  the  diurnal  motion  ;  east,  in  the  opposite  direction.  In  Fig.  2,  the  arrows 
all  point  west,  and  by  examining  the  figure  it  will  be  seen  that  below  the  pole 
north  is  upwards,  and  east  is  towards  the  west  horizon.  Really,  these  definitions 
hold  equally  true  for  the  earth,  the  same  differences  being  found  between  the 
points  of  the  compass  at  different  places  on  the  earth — here  and  in  China,  for  in- 
stance— that  we  see  on  the  celestial  sphere. 

29 


432  THE  STELLAR   UNIVERSE. 

the  north-west,  the  latter  in  the  north-east.  The  Milky  Way 
spans  the  lieavens  like  an  arch,  resting  on  the  horizon  in  the 
north-north-west  and  south-south-east.  We  shall  first  describe 
the  constellations  in  its  course. 

Cygnus,  the  Swan,  is  sinking  below  the  horizon,  where  the 
Milky  Way  rests  upon  it  in  the  north-north-west,  and  only  a 
few  stars  of  it  are  visible.  It  will  be  better  seen  at  another 
season. 

Next  in  order  come  Cepheus,  Cassiopeia,  and  Perseus,  which 
we  have  ah-eady  described  as  circunipolar  constellations. 

Above  Perseus  lies  Auriga^  the  Charioteer,  which  may  be 
readily  recognized  by  a  bright  star  of  the  fii'st  magnitude, 
called  Capella,  the  Goat,  now  a  few  degrees  north-west  of  the 
zenith.  Auriga  is  represented  as  holding  a  goat  in  his  arm, 
in  the  body  of  which  this  star  is  situated.  About  ten  degrees 
east  of  Capella  is  the  star  j3  Auriga  of  tlie  second  magnitude; 
while  still  farther  to  the  east  is  a  group  of  small  stars  which 
also  belongs  to  the  same  constellation.  The  latter  extends 
some  distance  south  of  the  zenith. 

The  Milky  Way  next  passes  between  Taurus  and  Gemini, 
which  we  will  describe  presently,  and  then  crosses  the  equator 
east  of  Orion,  the  most  brilliant  constellation  in  the  heavens, 
havinor  two  stars  of  the  first  magnitude  and  four  of  the  second. 
The  former  are  Betelguese,  or  a  Orionis,  which  is  highest  up, 
and  may  be  recognized  by  its  reddish  color,  and  liigel,  or  |3 
Orionis,  a  sparkling  white  star,  lower  down,  and  a  little  to  the 
west.  The  former  is  in  the  shoulder  of  the  figure,  tlie  latter 
in  the  foot.  Between  the  two,  three  stars  of  the  second  mag- 
nitude, in  a  row,  form  the  belt  of  the  warrior. 

Canis  Ifinor,  the  Little  Dog,  lies  just  across  the  Milky  Way 
from  Orion,  and  may  be  recognized  by  tlie  bright  star  Pre- 
cyon,  of  the  first  magnitude,  due  east  from  Betelguese. 

Canis  Major,  the  Great  Dog,  lies  south-east  of  Orion,  and  is 
easily  recognized  by  Sirius,  the  brightest  fixed  star  in  the  lieav- 
ens. A  number  of  bright  stars  south  and  south-east  of  Sirius 
belong  to  this  constellation,  making  it  one  of  great  brillianc}'. 

As  the  Milky  Way  approaches  the  south  horizon,  it  passes 


DESCBiniON  OF  THE  PRINCIPAL  CONSTELLATIONS.     433 

through  Argo  Navis,  the  Ship  Argo,  which  is  partly  below  the 
horizon.  It  contains  Canopus,  the  next  brightest  star  to  Siri- 
us ;  but  this  object  is  below  the  horizon,  unless  the  observer  is 
as  far  south  as  35°  of  north  latitude. 

We  can  next  trace  such  of  the  zodiacal  constellations  as  are 
high  enough  above  the  horizon.  In  the  west,  one-tliird  of  tlie 
way  from  the  horizon  to  the  zenith,  will  be  seen  Aries,  the 
Ram,  whicli  may  be  recognized  by  three  stars  of  the  second, 
third,  and  fourth  magnitudes,  respectively,  forming  an  obtuse- 
angled  triangle,  the  brightest  star  being  the  highest.  The 
arrangement  of  these  stai's,  and  of  some  others  of  the  fifth 
magnitude,  may  be  seen  by  Map  II. 

Taurus,  the  Bull,  is  next  above  Aries,  and  may  be  recog- 
nized by  the  Pleiades,  or  "  seven  stars,"  as  the  group  is  com- 
monly called.  Really  there  are  only  six  stars  in  the  group 
clearly  visible  to  ordinary  eyes,  and  an  eye  which  is  good 
enough  to  see  seven  will  be  likely  to  see  four  others,  or  eleven 
in  all.  A  telescopic  view  of  this  group  will  be  given  in  con- 
nection with  the  subject  of  clusters  of  stars.  Another  group 
in  this  constellation  is  the  Hyades,  the  principal  stars  of  which 
are  arranged  in  the  form  of  the  letter  V,  one  extremity  of  the 
V  being  formed  by  Aldebaran,  a  red  star  ranked  as  of  the 
first  magnitude,  but  not  so  bright  as  a  Orionis. 

Gemini,  the  Twins,  lies  east  of  the  Milky  Way,  and  may  be 
found  on  the  left  side  of  Map  II.  and  the  right  of  Map  III. 
The  brightest  stars  of  this  constellation  are  Castor  and  Pollux, 
or  a  and  (5,  which  lie  twenty  or  thirty  degrees  south-east  or 
east  of  the  zenith,  about  one-fourth  or  one-third  of  the  way 
to  the  horizon.  They  are  almost  due  north  from  Procyon ; 
that  is,  a  line  drawn  from  Procyon  to  the  pole  star  passes  be- 
tween them.  The  constellation  extends  from  Castor  and  Pol- 
lux some  distance  south  and  west  to  the  borders  of  Orion. 

Cancer,  the  Crab,  lies  east  of  Gemini,  but  contains  no  bright 
star.  The  most  noteworthy  object  within  its  borders  is  Prfe- 
sepe,  a  group  of  stars  too  small  to  be  seen  singly,  which  ap- 
pears as  a  spot  of  milky  light.  To  see  it  well,  the  night  must 
be  perfectly  clear,  and  the  moon  not  in  the  neighborhood. 


434:  THE  STELLAR   UNIVERSE. 

Leo,  the  Lion,  contains  the  bright  star  Regulus,  about  two 
hours  above  the  eastern  horizon.  This  star,  with  five  or  six 
smaller  ones,  forms  a  sickle,  Regulus  being  the  handle.  The 
sickle  is  represented  as  in  the  breast,  neck,  and  head  of  the 
lion,  his  tail  extendh)g  nearly  to  the  horizon,  where  it  ends  at 
the  star  Denebola,  now  just  risen. 

Such  are  the  principal  constellations  visible  in  the  supposed 
position  of  the  celestial  sphere.  If  the  houi*  of  observation  is 
different  from  that  supposed,  the  positions  of  the  constellations 
will  be  different  by  the  amount  of  diurnal  rotation  during  the 
interval.  For  instance,  if,  in  the  middle  of  March,  we  study 
the  heavens  at  eight  o'clock  instead  of  six,  tlie  western  stai*s 
will  be  nearer  the  horizon,  the  southern  ones  farther  west,  and 
the  eastern  ones  higher  up  than  we  have  described  them. 

Second  Position  of  the  Celestial  Sphere.  —  The  meridian  in 
twelve  hours  of  right  ascension,  near  the  left-hand  edge  of 
Map  III.,  and  the  right-hand  edge  of  Map  IV.  The  stai-s  on 
Map  III.  are  west  of  the  meridian,  those  of  Map  IV.  east  of  it. 
This  position  occurs  on 

March  21st at  midnight. 

April  20th at  10  o'clock. 

May  21st at  8  o'clock. 

In  this  position  Ursa  Major  is  near  the  zenith,  and  Cassiopeia 
in  the  north  horizon.  The  Milky  Way  is  too  near  the  horizon 
to  be  visible ;  Orion  has  set  in  the  west ;  and  there  are  no  very 
conspicuous  constellations  in  the  south.  Castor  and  Pollux  are 
visible  in  the  north-west,  at  a  considerable  altitude,  and  Pro- 
cyon  in  the  west,  about  an  hour  and  a  half  above  the  horizon. 
Leo  is  west  of  the  meridian,  extending  nearly  to  it,  while  three 
new  zodiacal  constellations  have  come  into  sight  in  the  east. 

Virgo.,  the  Virgin,  has  a  single  bright  star — Spica — about 
the  brilliancy  of  Regulus,  now  about  one  hour  east  of  the  me- 
ridian, and  a  little  more  than  half-way  from  the  zenith  to  the 
horizon. 

Libra,  the  Balance,  has  no  stars  which  will  attract  attention. 
The  constellation  may  be  recognized  by  its  position  between 
Virgo  and  Scorpius. 


DESCRIPTION  OF  THE  PRINCIPAL  CONSTELLATIONS.     435 

Scorpius,  the  Scorpion,  is  just  rising  in  the  south-east,  and  is 
not  yet  high  enough  to  be  well  seen. 

Amons  the  constellations  north  of  the  zodiac  we  have : 

Coma  Berenices^  the  Hair  of  Berenice,  now  exactly  on  the 
meridian,  and  about  ten  degrees  south  of  the  zenith.  It  is  a 
close,  irregular  group  of  very  small  stars,  quite  different  from 
anything  else  in  the  heavens.  In  the  ancient  mythology,  Ber- 
enice had  vowed  her  hair  to  the  goddess  Venus ;  but  Jupiter 
carried  it  away  from  the  temple  in  which  it  was  deposited, 
and  made  it  into  a  constellation, 

Bootes,  the  Bear-keeper,  is  a  large  constellation  east  of  Coma. 
It  is  marked  by  Arcturus,  a  very  bright  but  somewhat  red 
star,  an  hour  and  a  half  east  of  Coma  Berenices. 

Canes  Venatici,  the  Hunting  Dogs,  are  north  of  Coma.  They 
are  held  in  a  leash  by  Bootes,  and  are  chasing  Ursa  Major 
round  the  pole. 

Corona  Borealis,  the  Northern  Crown,  lies  next  east  of  Bootes 
in  the  nortli-east.  It  is  principally  composed  of  a  pretty  semi- 
circle of  stars,  supposed  to  form  a  chaplet,  or  crown. 

Third  Position  of  the  Sphere. — The  southern  constellations 
are  those  shown  on  Maps  IV.  and  V.,  those  of  Map  IV.  being 
west  of  the  meridian,  and  those  of  Map  V.  east  of  it.  This 
position  occurs  on 

June  21st at  midnight. 

July  21st at  10  o'clock. 

August  21st at  8  o'clock. 

etc etc. 

In  this  position  the  Milky  Way  is  once  more  in  sight,  and 
seems  to  span  the  heavens,  but  we  do  not  see  the  same  ])art 
of  it  which  was  visible  in  the  first  position.  Cassiopeia  is" 
now  in  the  north-east,  and  Ursa  Major  has  passed  over  to  the 
north-west.  Arcturus  is  two  or  three  hours  higli  in  the  west, 
and  Corona  is  above  it,  two  or  three  hours  west  of  the  zenith. 
Commencing,  as  in  the  first  position,  with  the  constellations 
wliich  lie  along  the  Milky  Way,  we  start  upwards  from  Cas- 
siopeia, pass  Cepheus  and  Lacerta,  neither  of  which  contains 
any  striking  stars,  and  then  reacli 


436  THE  STELLAR   UNIVERSE. 

Cygnus,  the  Swan,  now  nortli-east  from  the  zenith,  -which 
may  be  recognized  by  four  or  iive  stars  forming  a  cross,  di- 
rectly in  the  Milky  Way.  The  brightest  of  these  stai-s  some- 
what exceeds  the  brightest  ones  of  Cassiopeia. 

Lyra^  the  Harp,  is  west  and  south-west  of  Cygnus,  and  near 
the  zenith.  It  contains  the  bright  star  Vega,  or  a  Lyrae,  of 
the  first  magnitude,  of  a  brilliant  white  color  with  a  tinge  of 
blue. 

Passing  south,  over  Yulpecida,  the  Little  Fox,  and  Sagittay 
the  Arrow,  the  next  striking  constellation  we  reach  is 

Aquila,  the  Eagle,  now  midway  between  the  zenith  and  the 
horizon,  and  two  hours  east  of  the  meridian.  It  contains  a 
bright  star  —  Altair,  or  a  Aquil^e  —  situated  between  two 
smaller  ones,  the  row  of  three  stars  running  nearly  north  and 
south. 

We  next  pass  west  of  the  Milky  Way,  and  direct  our  atten- 
tion to  a  point  two  hours  west  of  the  meridian,  and  some  dis- 
tance towards  the  south  horizon.     Here  we  find 

Sco/yius,  the  Scorpion,  a  zodiacal  constellation  and  a  quite 
brilliant  one,  containing  Antares,  or  a  Scorpii,  a  reddish  star 
of  nearly  the  first  magnitude,  with  a  smaller  star  on  each  side 
of  it,  and  a  long  curved  row  of  stars  to  the  west. 

Sagittarius,  the  Archer,  comprises  a  large  collection  of  sec- 
ond-magnitude stars  east  of  Scorpius,  and  in  and  east  of  the 
Milky  Way,  and  now  extending  from  the  meridian  to  a  point 
two  hours  east  of  it. 

Capricornus,  the  Goat,  another  zodiacal  constellation,  is  now 
in  the  south-east,  but  contains  no  striking  stars.  The  same 
remark  applies  to  Aquarius,  the  Water-bearer,  which  has  just 
risen,  and  Pisces,  the  Fishes,  partly  below  the  eastern  horizon. 

Leaving  the  zodiac  again,  we  find,  north  of  Scorpius  and 
west  of  the  Milky  Way,  a  very  large  pair  of  constellations, 
called  Ophiuchus,  the  Serpent-bearer,  and  Serpens,  the  Serpent. 
Ophiuchus  stands  with  one  foot  on  Scorpius,  while  his  head  is 
marked  by  a  star  of  the  second  magnitude  twelve  degrees 
north  of  the  equator,  and  now  on  the  meridian.  It  is,  there- 
fore. Qne-third  or  one-fourth  of  the  way  from  the  zenitb  to  the 


DESCRIPTION  OF  THE  PRINCIPAL  CONSTELLATIONS.     437 

horizon.  The  Serpent,  which  he  holds  in  his  hands,  hes  with 
its  tail  in  an  opening  of  the  Milky  Way,  south-west  of  Aqiiila, 
wliile  its  neck  and  head  arc  formed  by  a  collection  of  stars  oi 
the  second,  third,  and  foui-th  magnitudes  some  distance  north 
of  Scorpius,  and  extending  up  to  the  borders  of  Bootes. 

Hercules  is  a  very  large  constellation,  bounded  by  Corona 
on  the  west,  Lyra  on  the  east,  Ophiuchus  on  the  south,  and 
Draco  on  the  north.  It  is  now  in  the  zenith,  but  contains  no 
striking  stars. 

Draco,  i\\Q  Dragon,  lies  with  his  head  just  nortli  of  Hercules, 
while  his  body  is  marked  by  a  long  curved  row  of  stars  ex- 
tending round  the  pole  between  the  Gi-eat  and  the  Little  Bear. 
His  head  is  readily  recognized  by  a  collection  of  stars  of  the 
second  and  third  magnitudes  which  might  well  suggest  such 
an  object. 

Fourili  Posilion  of  the  Sphere. — The  southern  constellations 
are  now  found  on  Maps  V.  and  IL — those  of  Map  V.  west  of 
the  meridian,  those  of  Map  II.  east  of  it.     The  times  are : 

September  21st at  midnight. 

October  21st at  10  o'clock. 

November  20tli at  8  o'clock. 

December  21st at  6  o'clock. 

In  this  position  Cassiopeia  is  just  nortli  of  the  zenitli,  while 
Ursa  Major  is  glimmering  in  the  north  horizon.  Following 
the  Milky  Way  from  Cassiopeia  towards  the  west,  we  shall 
cross  Cepheus,  Cygnus,  Lyra,  and  Aquila,  wliile  towards  the 
east  we  pass  Perseus  and  Auriga,  all  of  which  ha\e  been  de- 
scribed. 

In  the  south,  the  principal  constellation  is  Pegasus,  the  Fly- 
ifig  Horse,  distinguished  by  four  stars  of  the  second  magni- 
,tude,  which  form  a  large  square,  each  side  of  which  is  about 
'fourteen  degrees. 

Andromeda,  her  hands  in  chains,  is  readily  found  by  a  row 
of  three  bright  stars  extending  north-east  from  the  north-east 
corner  of  Pegasus  in  the  direction  of  Perseus. 

Cehis,  the  Whale,  is  a  large  constellation  in  the  south,  ex- 
tending from  the  meridian  to  a  point  three  hours  east  of  it. 


438  THE  STELLAR   UNIVERSE. 

Its  brightest  stars  are  B  Ceti,  now  near  the  meridian,  at  an  al« 
titude  of  20°,  which  stands  by  itself,  and  a  Ceti,  about  20°  be- 
low Aries,  which  is  now  about  30°  south-east  from  the  zenith. 
The  reader  who  wishes  to  consult  the  constellations  in 
greater  detail  can  readily  do  so  by  means  of  the  star-maps. 

§  3.  New  and  Variable  Stars. 

The  large  majority  of  stai-s  always  appear  to  be  of  the  same 
brightness,  though  it  is  quite  possible  that,  if  the  quantity  of 
light  emitted  by  a  star  could  be  measured  with  entire  preci- 
sion, it  would  be  found  in  all  cases  to  vary  slightly,  from  time 
to  time.  There  are,  however,  quite  a  number  of  stars  in  which 
the  variation  is  so  decided  that  it  has  been  detected  by  com- 
paring their  apparent  brightness  with  that  of  other  stars  at  dif- 
ferent times.  More  than  a  hundred  such  stars  are  now  known; 
but  in  a  large  majority  of  cases  the  variation  is  so  slight  that 
only  careful  observation  with  a  practised  eye  can  percei^■e  it. 
There  are,  however,  two  stars  in  which  it  is  so  decided  that 
the  most  casual  observer  has  only  to  look  at  the  proper  times, 
in  order  to  see  it.  These  are  j3  Persei  and  o  Ceti,  or  Algol 
and  Mira,  to  which  we  might  add  rj  Argus,  a  star  of  the  south- 
ern hemisphere,  which  exhibits  variations  of  a  very  striking 
character. 

Variations  of  Algol. —  This  star,  marked  /3  in  the  constel- 
lation Perseus,  may  be  readily  found  on  Maps  I.  and  II.,  in 
right  ascension  3  hours  and  declination  40°  23'.  When  once 
found,  it  is  readily  recognized  b}'  its  position  nearh'  in  a  line 
between  two  smaller  stars.  The  most  favorable  seasons  for 
seeing  it  in  the  early  evening  are  the  autumn,  winter,  and 
spring.  In  autumn  it  will,  after  sunset,  generally  be  low 
down  in  the  north-east;  in  wintei-,  high  up  in  the  north,  not 
far  from  the  zenith ;  and  in  spring,  low  down  in  the  north. 
west.  Usually  it  shines  as  a  faint  second-magnitude  star :  on 
an  accurate  scale  the  magnitude  is  about  2^.  But  at  inter- 
vals of  a  little  less  than  three  days,  it  fades  out  to  the  fourth 
magnitude  for  a  few  houi*s,  and  then  resumes  its  usual  splen- 
dor once  more.     These  changes  were  first  noticed  about  two 


!^UW  AND  VARIABLE  STARS.  439 

centuries  ago,  but  it  was  not  till  1782  that  thej  were  accu- 
rately observed.  The  period  is  now  known  to  be  2  da3-s,  20 
hours,  49  minutes.  It  was  long  ago  suggested  tiiat  this  phe- 
nomenon was  a  partial  eclipse  of  the  star  by  a  dark  planet  re- 
volving around  it.  This  view  has  been  confirmed  in  a  remark- 
able way  by  the  researches  of  Dr.  Vogel  at  Potsdam,  by  deter- 
mining its  motion  in  the  line  of  sight,  as  explained  in  §  7  of 
this  chapter.  He  found  that  before  each  eclipse  the  star  was 
moving  away  from  the  earth,  and  after  it  toward  the  earth. 
Such  an  alternation  of  motions  could  only  arise  from  the  at- 
traction of  a  revolving  body ;  and  the  eclipses  occur  as  the 
body  is  shown  to  be  on  this  side  of  the  star.  The  same  obser- 
vations enabled  him  to  find  approximately  the  size  of  both 
star  and  planet  and  the  velocity  of  the  latter  in  its  orbit. 

Formerly  the  variation  of  the  period  offered  a  difficulty  in 
accepting  this  explanation,  but  this  difficulty  was  resolved  in 
a  most  happy  way  by  Mr.  S.  C.  Chandler,  of  Cambridge,  who 
showed  that  Algol  was  probably  revolving  round  yet  another 
unseen  body  in  a  period  of  more  than  a  century.  When  com- 
ing toward  us  in  its  orbit,  the  period  would  be  shorter  be- 
cause the  star  would  partly  overtake  the  light  by  which  we 
see  it,  when  moving  away  longer,  because  the  light  would 
have  farther  to  travel  after  each  successive  eclipse. 

Another  remarkable  variable  star,  but  of  an  entirely  differ- 
ent type,  is  o  Ceti,  or  Mira  (the  Wonderful).  It  may  be  found 
on  Map  II.,  in  right  ascension  2  hours  12  minutes,  declination 
3°  39'  south.  During  most  of  the  time  this  star  is  entirely 
invisible  to  the  naked  eye,  but  at  intervals  of  about  eleven 
months  it  shines  forth  with  the  brilliancy  of  a  star  of  the  sec- 
ond or  third  magnitude.  It  is,  on  the  average,  about  forty 
days  from  the  time  it  first  becomes  visible  until  it  attains  its 
greatest  brightness,  and  it  then  requires  about  two  months  to 
become  invisible ;  so  that  it  comes  into  sight  more  rapidly 
than  it  fades  away.  It  is  expected  to  attain  its  greatest  brill- 
iancy in  November,  1877 ;  in  October,  1878,  and  so  on,  about 
a  month  earlier  each  year;  but  the  period  is  quite  irregular, 
ranging  from  ten  to  twelve  months,  so  that  the  times  of  its 


440 


THE  STELLAR   VNIVERSE. 


appearance  cannot  be  predicted  with  certainty.  Its  maximum 
brilliancy  is  also  variable,  being  sometimes  of  the  second  mag- 
nitude, and  at  othei^s  only  of  the  third  or  fourth. 

Tj  Anjus. — Perhaps  the  most  extraordinary  known  variable 
star  in  the  heavens  is  ij  Argus,  of  the  southern  hemisphere,  of 
which  the  position  is,  right  ascension,  10  hours  40  minutes; 
declination,  59^  1'  south.  Being  so  far  south  of  the  equator, 
it  cannot  be  seen  in  our  latitudes,  and  the  discovery  and  ob- 
servations of  the  variations  of  its  light  have  been  generally 
made  by  astronomers  who  have  visited  the  soutlieru  hemi- 
sphere. In  1677,  Halley,  while  at  St.  Helena,  found  it  to  be 
of  the  fourth  magnitude.  In  1751,  Lacaille  found  that  it  had 
increased  to  the  second  magnitude.  From  1S2S  to  1S3S  it 
ranged  between  the  first  and  second  magnitudes.  The  firet 
careful  observations  of  its  variability  were  made  by  Sir  John 
Herschel  while  at  the  Cape  of  Good  Hope.  He  says :  "  It 
was  on  the  16th  December,  1837,  that,  resuming  the  photo- 
metrical  comparisons,  my  astonishment  was  excited  by  the  ap- 
pearance of  a  new  candidate  for  distinction  among  the  very 
brightest  stai*s  of  the  first  magnitude  in  a  part  of  the  heav- 
ens with  which,  being  perfectly  familiar,  I  was  certain  that  no 
Buch  brilliant  object  had  before  been  seen.  After  a  momen- 
tary hesitation,  the  natural  consequence  of  a  phenomenon  so 
utterly  unexpected,  and  referring  to  a  map  for  its  configura- 
tion with  other  conspicuous  stars  in  the  neighborhood,  I  be- 
came satisfied  of  its  identity  with  my  old  acquaintance,  »/  Ar- 
gus. Its  light,  was,  however,  nearly  tripled.  While  yet  low, 
it  equalled  liigel,  and,  when  it  attained  some  altitude,  was 
decidedly  greater."*  Sir  John  states  that  it  continued  to  in- 
crease until  January  2d,  1S3S.  when  it  was  nearly  matched 
with  a  Centauri.  It  then  faded  a  little  till  the  close  of  his 
observations  in  April  followinir.  hut  was  still  as  bright  as  Al- 
debaran.  But  in  1842  and  1S43  it  blazed  up  brighter  than 
ever,  and  in  March  of  the  Jatter  year  was  second  only  to 
Sirius.     During  the  twenty-fi\e  years  following,  it  slowly  but 

*  "Astronomical  Observations  at  the  Cape  of  Good  Hope,"  p.  33. 


NEW  AND  VARIABLE  STAIiS.  441 

steadily  diminished  :  in  1 867  it  was  barely  visible  to  the  naked 
eye,  and  the  year  following  it  vanished  entirely  from  the  un- 
assisted view,  and  has  not  yet  begun  to  recover  its  brightness. 

When  we  speak  of  this  star  as  the  most  remarkable  of  the 
well-known  variables,  we  refer,  not  to  the  mere  range  of  its 
variations,  but  to  its  brilliancy  when  at  its  maximum.  Sev- 
eral eases  of  equally  great  variation  are  known ;  but  the  stars 
are  not  so  bright,  and  therefore  would  not  excite  so  much  no- 
tice. Thus,  the  star  R  Andromeda3  varies  from  the  sixth  to 
the  thirteenth  magnitude  in  a  pretty  regular  period  of  405 
days.  When  at  its  brightest,  it  is  just  visible  to  the  naked 
eye,  while  only  a  large  telescope  will  show  it  when  at  its  min- 
imum. A.  number  of  others  range  through  five  or  six  orders 
of  magnitude,  but  o  Ceti  is  the  onl}'  one  of  these  which  ever 
becomes  as  bright  as  the  second  magnitude. 

The  foregoing  stars  are  the  only  ones  the  variations  of 
which  would  strike  the  ordinary  observer.  Among  the  hun- 
dred remaining  ones  which  astronomers  have  noticed,  j3  Lyrse 
is  remarkable  for  having  two  maxima  and  two  minima  of  un- 
equal brilliancy.  If  we  take  it  when  at  its  greatest  minimum, 
we  find  its  magnitude  to  be  4|-.  In  tlie  coui'se  of  three  days, 
it  will  rise  to  magnitude  3^.  In  the  course  of  the  week  fol- 
lowing, it  will  first  fall  to  the  fourth  magnitude,  and  increase 
again  to  magnitude  3h  In  three  days  more  it  will  drop 
again  to  its  minimum  of  magnitude  4^^;  the  period  in  which 
it  goes  through  all  its  changes  being  thirteen  days.  This  pe- 
riod is  constantly  increasing.  The  changes  of  this  star  can 
best  be  seen  by  comparing  it  with  its  neighbor,  7  Lyi-a3.  Some- 
times it  M'ill  appear  equally  bright  with  the  latter,  and  at  other 
times  a  magnitude  smaller.* 

*  In  1875,  Professor  Schonfeld,  now  director  of  the  observatory  at  Bonn,  pub- 
lished a  complete  catalogue  of  known  variable  stars,  the  total  number  being  143. 
The  following  are  the  more  remarkable  ones  of  his  list.  The  positions  are  re- 
ferred to  the  ecliptic  and  equinox  of  187.") : 

T  Cassiopeiie:  right  ascension,  0  hours  IG  minutes  20  seconds;  declination,  r^n° 
fi'.O  N. — This  is  a  case  in  which  a  star,  having  once  been  observed,  wns  after- 
wards found  to  be  missing.  Examination  showed  that  it  had  so  far  diminished 
as  to  be  no  longei  visible  -vithout  a  larger  telesicope,  and  continued  observations 


.j42  THE  STELLAR   UXIVEBSE. 

Keic  Stars. — It  was  once  supposed  to  be  no  uncommon  occur- 
rence for  new  stars  to  come  into  existence  and  old  ones  to  dis- 
appear, the  former  being  looked  upon  as  new  creations,  and 
the  disappearances  as  due  to  the  destruction  or  annihilation 
of  those  stars  which  had  fulfilled  their  end  in  the  econom}-  of 
nature.  The  supposed  disappearances  of  stai-s  are,  however, 
found  to  have  no  certain  foundation  in  fact,  probably  owing 
their  origin  to  errors  in  recording  the  position  of  stai*s  actu- 
ally existing.  It  was  explained,  in  treating  of  Practical  As- 
tronomy, that  the  astronomer  determines  the  position  of  a 
body  in  the  celestial  vault  by  observing  the  clock- time  at  which 
it  passes  the  meridian,  and  the  position  of  the  circle  of  his  in- 
showed  it  to  range  from  the  seventh  to  the  eleventh  magnitude  with  a  regular 
period  of  436  days. 

B  Cassiopeise  :  right  ascension,  0  hours  17  minutes  52  seconds  ;  declination, 
63^  27. 0  X. — This  is  supposed  to  be  the  celebrated  star  which  blazed  out  in 
November,  1572,  and  was  so  fullv  described  by  Tycho  Brahe.  But  the  proof  of 
identity  can  hardly  be  considered  conclusive,  especially  as  no  variation  has,  of  re- 
cent years,  been  noticed  in  the  star. 

o  Ceti :  right  ascension.  2  hours  13  minutes  1  second;  declination,  3^  32*.  7 
S. — We  have  already  described  the  variations  of  this  star. 

/3  Persei,  or  Algol :  right  ascension,  3  hours  0  minutes  2  secands  ;  declina- 
tion, -tO^  2S'.4  X. — Tiie  variations  of  this  star,  which  is  the  most  regular  one 
known,  have  just  been  described. 

R  Auriga?:  right  ascension,  5  hours  7  minutes  12  seconds;  declination,  53" 
26'.6  X. — This  star  is  one  of  very  wide  and  complex  variation,  changing  from  the 
sixth  to  the  thirteenth  magnitude  in  a  period  of  about  4G5  days. 

R  Gemiuorum :  right  ascension,  6  hours  50  minutes  49  seconds;  declination, 
22^  53'. 8  X. — This  star  was  discovered  by  ^Ir.  Hind,  of  England,  and  ranges  be- 
tween the  seventh  and  the  twelfth  magnitude  in  a  period  of  371  days. 

U  Geminorum :  right  ascension,  7  hours  47  minntes  41  seconds ;  declination, 
22°  19'.  7  X. — An  irregular  variable,  never  visible  to  tiie  naked  eye,  remarkable 
for  the  rapidity  with  which  it  sometimes  changes.  Schijnfeld  says  that  in  Feb- 
ruary, 1869.  it  increased  three  entire  magnitudes  in  24  hours.  The  periods  of  its 
greatest  brightness  have  ranged  from  75  to  617  days. 

t)  Argus :  right  ascension,  10  hours  40  minntes  13  seconds ;  declination,  59° 
I'.G  S. — This  remarkable  object  has  already  been  described. 

R  Hydrje :  right  ascension,  13  hours  22  minntes  53  seconds;  declination,  22' 
38'. 0  S. — The  variability  of  this  star  was  recognized  by  ilaraldi,  in  1704.  It  is 
generally  invisible  to  the  naked  eye,  but  rises  to  about  the  fiftli  magnitude  at 
intervals  of  about  437  days.  Its  period  seems  to  be  diminishing,  having  been 
about  500  davs  when  first  discovered. 


NEW  AND   VARIABLE  STARS.  443 

strument  when  his  telescope  is  pointed  at  the  object.  If  he 
happens  to  make  a  mistake  in  writing  down  any  of  these 
numbers — if,  for  example,  he  gets  his  clock-time  one  minute 
or  five  minutes  wrong,  or  puts  down  a  wrong  number  of  de- 
grees for  the  position  of  his  circle — he  will  write  down  the 
position  of  the  star  where  none  really  exists.  Then,  some  sub- 
sequent astronomer,  looking  in  this  place  and  seeing  no  star, 
may  think  the  star  has  disappeared,  when,  in  reality,  there  was 
never  any  star  there.  Where  thousands  of  numbei"s  have  to  be 
written  down,  such  mistakes  will  sometimes  occur;  and  it  is  to 
them  that  some  cases  of  supposed  disappearance  of  stars  are  to 
be  attributed.  There  have,  however,  been  several  cases  of  ap- 
parently new  stars  coming  suddenly  into  view,  of  which  we 
shall  describe  some  of  the  most  remarkable. 

T  CoroDis :  right  ascension,  15  hours  54  minutes  16  seconds;  declination,  26^ 
16'. 5  N. — This  is  the  "new  star"  which  blazed  out  in  the  Northern  Crown  in 
1866,  as  hereafter  described.  Of  late  years  it  has  remained  between  the  ninth 
and  tenth  magnitudes  without  exliibiting  any  remarkable  variations. 

T  Scorpii :  right  ascension,  16  liours  9  minutes  36  seconds ;  declination,  22'' 
40'.0  S. — This  star  was  discovered  by  Auwers,  in  1860,  in  the  midst  of  a  well- 
known  cluster.  It  gradually  diminished  during  the  following  months,  and  finally 
disappeared  entirely  among  the  stars  by  which  it  is  surrounded. 

—  Serpentarii :  right  ascension,  17  hours  23  minutes  9  seconds ;  declination, 
21°  22'. 4  S. — This  is  supposed  to  be  the  celebrated  "new  star"  seen  and  de- 
scribed by  Kepler  in  1604,  soon  to  be  described. 

X  Cygni:  right  ascension,  19  hours  45  minutes  46  seconds;  declination,  32^  3(]'.n 
N. — Tills  star  becomes  visible  to  the  naked  eye  at  intervals  of  about  406  days,  and 
then  sinks  to  the  twelftli  or  thirteenth  magnitude,  so  that  only  large  telescopes  will 
show  it.     Its  greatest  brightness  ranges  from  the  fourth  to  the  sixth  magnitude. 

t]  Aquili«  :  right  ascension,  19  hours  46  minutes  6  seconds ;  declination,  0' 
41'.  2  N. — This  star  vaiies  from  magnitude  'i\  to  4f,  and  is  therefore  one  of 
those  whicli  can  readily  be  observed  with  the  naked  eye.  Its  period  is  7  days  4 
hours  14  minutes  4  seconds. 

P  Cygni:  right  ascension,  20  hours  13  minutes  11  seconds;  declination,  o7° 
38'.7  N. — This  was  supposed  to  be  a  new  star  in  16D0,  when  it  was  first  seen 
by  Janson.  During  the  remainder  of  the  century  it  varied  from  the  third  to  the 
sixth  magnitude ;  but  during  two  centuries  which  have  since  elapsed  no  further 
variations  have  been  noticed,  the  star  being  constantly  of  the  fifth  magnitude. 

fi  Cephei:  right  ascension,  21  hours  39  minutes  41  seconds;  declination,  58" 
12'.4  N. — One  of  the  reddest  stars  visible  to  the  naked  eye  in  the  northern  hemi* 
sphere.  Its  magnitude  is  found  to  vary  from  the  fourth  to  the  fifth  in  a  very  iii 
vegular  manner. 


.i44  THE  STELLAR   UNIVERSE. 

In  1572  an  apparently  new  star  sliowed  itself  in  Cassiopeia. 
It  was  first  seen  by  Tycho  Bralie  on  November  11th,  when 
it  had  attained  the  first  magnitude.  It  increased  rapidly  in 
brilliancy,  soon  becoming  equal  to  Yenus,  so  that  good  eyes 
conld  discern  it  in  full  daylight.  In  December  it  began  to 
grow  smaller,  and  continued  gradually  to  fade  away  nntil  the 
month  of  March,  1574,  when  it  became  invisible.  This  was 
forty  years  before  the  invention  of  the  telescope.  Tycho  has 
left  us  an  extended  treatise  on  this  most  remarkable  star. 

In  1601  a  similar  phenomenon  was  seen  in  the  constella- 
tion Ophiuchus.  The  star  was  first  noticed  in  October  of  that 
year,  when  it  had  attained  the  first  magnitude.  In  the  follow- 
ing winter  it  began  to  wane,  but  remained  visible  during  the 
whole  year  1605.  Early  in  1606  it  faded  away  entirely,  hav- 
ing been  visible  for  more  than  a  year.  A  very  full  history  of 
this  star  has  been  left  to  us  by  Kepler. 

The  most  striking  recent  case  of  this  kind  was  in  Ma}', 
1866,  when  a  star  of  the  second  magnitude  suddenly  appeared 
in  Corona  Borealis.  On  the  11th  and  12th  of  that  month  it 
was  remarked  independently  by  at  least  five  observers  in  Eu- 
rope and  America,  one  of  the  first  being  Mr.  Farquliar,  of  the 
United  States  Patent-ofiice.  Whether  it  really  blazed  out  as 
suddenly  as  this  would  indicate  has  not  been  definitively  set- 
tled. If,  as  would  seem  most  probable,  it  was  several  days 
attaining  its  greatest  brilliancy,  then  the  only  person  known 
to  have  seen  it  was  Mr.  Benjamin  Hallowell,  a  well-known 
teacher  near  "Washington,  whose  testimony  is  of  such  a  nature 
that  it  is  hard  to  doubt  that  the  star  was  visible  several  days 
before  it  was  generally  known.  On  the  other  hand,  Schmidt, 
of  Athens,  asserts  in  the  most  positive  manner  that  the  star 
was  not  there  on  May  10th,  because  he  was  then  scanning 
that  part  of  the  heavens,  and  would  certainly  have  noticed  it. 
However  the  fact  may  have  been  in  this  particular  case,  it  is 
noteworthy  that  none  of  the  new  stars  we  have  described  were 
noticed  until  they  had  nearW  or  quite  attained  their  greatest 
brilliancy,  a  fact  which  gives  color  to  the  view  that  they  have 
all  blazed  up  with  great  rapidity. 


NEW  AND  VARIABLE  STARS.  445 

In  November,  18Y6,  a  new  star  of  tlie  third  magnitude  was 
noticed  by  Schmidt,  of  Athens,  in  the  constellation  Cygnns. 
It  soon  began  to  fade  away,  and  disappeared  from  the  unaided 
vision  in  a  few  weeks.  The  position  of  the  constellation  Cyg- 
nus  becomes  so  unfavorable  for  observation  in  November  that 
very  few  people  got  a  sight  of  this  object. 

The  view  that  these  bodies  may  be  new  creations,  designed 
to  rank  permanently  among  their  fellow-stars,  is  completely 
refuted  by  their  transient  character,  if  by  nothing  else.  Their 
apparently  ephemeral  existence  is  in  striking  contrast  to  the 
permanency  of  the  stars  in  general,  which  endure  from  age  to 
age  without  any  change  whatever.  They  are  now  classified 
by  astronomers  among  the  variable  stars,  their  changes  being 
of  a  very  irregular  and  fitful  character.  There  is  no  serious 
doubt  that  they  were  all  in  the  heavens  as  very  small  stars 
before  they  blazed  forth  in  this  extraordinary  manner,  and 
that  they  are  in  the  same  place  yet.  The  position  of  the  star 
of  1572  was  carefully  determined  by  Tycho  Brahe ;  and  a 
small  telescopic  star  now  exists  within  V  of  the  place  com- 
puted from  his  observations,  and  is  probably  the  same.  The 
star  of  1866  was  found  to  have  been  recorded  as  one  of  the 
ninth  magnitude  in  Argelander's  great  catalogue  of  the  stars 
of  the  northern  hemisphere,  completed  several  years  before. 
After  blazing  up  in  the  way  w^e  have  described,  it  gradually 
faded  away  to  its  former  insignificance,  and  has  shown  no 
further  signs  of  breaking  forth  again.  There  is  a  wide  diifer- 
ence  between  these  irregular  variations,  or  breaking-fortli  of 
light,  on  a  single  occasion  in  the  course  of  centuries,  and  the 
regular  changes  of  Algol  and  /3  Lyra3.  But  the  careful  obser- 
vations of  the  industrious  astronomers  who  have  devoted  them- 
selves to  this  subject  have  resulted  in  the  discovery  of  stars 
of  nearly  every  degree  of  irregularity  between  these  extremes. 
Some  of  them  change  gradually  from  one  magnitude  to  another, 
in  the  course  of  years,  without  seeming  to  follow  any  law  what- 
ever, while  in  others  some  tendency  to  regularity  can  be  faintly 
traced.  The  best  connecting  link  between  new  and  variable  stars 
is,  perhaps,  afforded  by  ij  Argus,  which  we  have  just  described 


446  THE  STELLAR   UNIVERSE. 

It  is  probable  that  the  variations  of  light  of  which  we  have 
spoken  are  the  result  of  operations  going  on  in  the  star  itself, 
wliich,  it  must  be  remembered,  is  a  body  of  the  same  order  of 
magnitude  and  brilliancy  with  our  sun,  and  that  these  opera- 
tions are  analogous  to  those  which  produce  the  solar  spots.  It 
was  shown  in  the  chapter  on  the  sun  that  the  frequency  of 
solar  spots  shows  a  period  of  eleven  years,  during  one  portion 
of  which  there  are  frequently  no  spots  at  all  to  be  seen,  while 
durhig  another  portion  they  are  very  nnmerous.  Hence,  if 
an  observer  so  far  away  in  the  stellar  places  as  to  see  our  sun 
like  a  star,  could,  from  time  to  time,  make  exact  measures  of 
the  amount  of  light  it  emitted,  he  would  lind  it  to  be  a  vari- 
able star,  with  a  period  of  eleven  years,  the  amount  of  light 
being  least  when  we  see  most  spots,  and  greatest  when  there 
are  few  spots.  The  variation  would,  indeed,  be  so  slight  that 
we  could  not  perceive  it  with  any  photometric  means  which 
we  possess,  but  it  would  exist  nevertheless.  Now,  the  general 
analogies  of  the  universe,  as  well  as  the  testimony  of  the  spec- 
troscope, lead  us  to  believe  that  the  physical  constitution  of 
the  sun  and  the  stars  is  of  the  same  general  nature.  We  may 
therefore  expect  that,  as  we  see  spots  on  the  sun  which  vary 
in  form,  size,  and  number  from  day  to  day,  so,  if  we  could 
take  a  sufficiently  close  view  of  the  faces  of  the  stars,  we 
should,  at  least  in  some  of  them,  see  similar  spots.  It  is  also 
likely  that,  owing  to  the  varying  physical  constitution  of  these 
bodies,  the  number  and  extent  of  the  spots  might  be  found  to 
be  very  different  in  different  stars.  In  the  cases  in  wliich  the 
spots  covered  the  larger  portion  of  the  surface,  their  variations 
in  number  and  extent  would  alone  cause  the  star  to  vary  in 
light,  from  time  to  time.  Finally,  we  have  only  to  suppose 
tlie  same  kind  of  regularity  which  we  see  in  the  eleven-3'ear 
aycle  of  the  solar  spots,  to  have  a  variation  in  the  brightness 
of  a  star  going  through  a  regular  cycle,  as  in  the  case  of  Algol 
and  Mira  Ceti. 

The  occasional  outbui-sts  of  stars  which  we  have  described, 
in  which  their  light  is  rapidly  increased  a  hundred-fold,  would 
seem  not  to  be  accounted  for  on  the  spot  theory,  without  car 


NEW  AND   VARIABLE  STARS.  447 

rying  this  theory  to  an  extreme.  It  would,  in  fact,  if  not 
modified,  imply  that  ninety-m'ne  parts  of  the  surface  out  of  a 
hundred  were  ordinarily  covered  with  spots,  and  that  on  rare 
occasions  these  spots  all  disappeared.  But  the  spectroscopic 
observations  of  the  star  of  1866  showed  an  analogy  of  a  little 
different  character  with  operations  going  on  in  our  sun.  Mr. 
Huggins  found  the  spectrum  of  this  star  to  be  a  continuou.-^ 
one,  crossed  by  bright  lines,  the  position  of  which  indicated 
that  they  proceeded  partly  or  wholly  fi-om  glowing  hydrogen. 
The  continuous  spectrum  was  also  ci'ossed  by  dark  absorption 
lines,  indicating  that  the  light  had  passed  tiiiough  an  atmos- 
phere of  comparatively  cool  gas.  J^r.  Ilnggins's  interpreta- 
tion of  this  is  that  there  was  a  sudden  and  extraordinary  out- 
burst of  hydrogen  gas  from  the  star  which,  by  its  own  light, 
as  well  as  by  heating  up  the  whole  surface  of  the  star,  caused 
the  immense  accession  of  bi'illiancy.  Now,  we  have  shown 
that  the  red  flames  seen  around  the  sun  during  a  total  eclipse 
are  caused  by  eruptions  of  hydrogen  from  his  interior;  more- 
over, these  eruptions  are  generally  connected  with  facula^,  or 
portions  of  the  sun's  disk  sevei-al  times  more  brilliant  than  the 
rest  of  the  photosphere.  Hence,  it  is  not  unlikely  that  the 
blazing-forth  of  this  star  arose  from  an  action  siuiilar  to  that 
M'hich  produces  the  solar  flames,  only  on  an  innnenselj-  larger 
scale. 

We  have  thus  in  the  spots,  faculse,  and  protuberances  of 
the  sun  a  few  suggestions  as  to  what  is  probahly  going  on  in 
those  stars  which  exhibit  the  extraordinary  changes  of  liijht 
which  we  have  described.  Is  there  any  possibility  that  oui- 
sun  may  be  subject  to  such  outbursts  of  light  and  heat  as 
those  we  have  described  in  the  cases  of  apparenth'  new  and 
temporary  stars?  We  may  almost  say  that  the  contimied  e\- 
istence  of  the  human  race  is  involved  in  this  question  ;  for  if 
the  heat  of  the  sun  should,  even  for  a  few  days  only,  be  in- 
creased a  hundred-fold,  the  higher  orders  of  animal  and  veg- 
etable life  would  be  destroyed.  "We  can  only  reply  to  it  that 
the  general  analogies  of  nature  lead  us  to  believe  that  we 
need  not  feel  any  apprehension  of  such  a  catastrophe.     Not 

30 


448  THE  STELLAR   UNIVERSE. 

the  slishtest  certain  variation  of  tlie  solar  lieat  has  been  de« 
tected  since  the  invention  of  the  thermometer,  and  the  gen- 
eral constancy  of  the  light  emitted  by  ninety-nine  stars  out  of 
every  hundred  may  inspire  ns  with  entire  confidence  that  no 
sudden  and  destructive  variation  need  be  feared  in  the  case 
of  our  Guu. 

§  4.  Double  Stars. 

Telescopic  examination  shows  that  many  stars  whijc-h  seem 
single  to  the  naked  eye  are  really  double,  or  composed  of  a 
pair  of  stars  lying  side  by  side.  There  are  in  the  heavens 
several  pairs  of  stars  tli^  components  of  which  are  so  close 
together  that,  to  the  naked  eye,  they  seem  almost  to  touch 
eacli  other.  One  of  the  easiest  and  most  beautiful  of  these 
is  in  Tanrns,  quite  near  Aldebaran.  Here  the  two  stars  0' 
Tauri  and  Q'^  Tauri  are  each  of  tlie  fourth  magnitude.  An- 
other such  pair  is  a  Capricorni,  in  which  the  two  stars  are  un- 
equal. Here  an  ordinary  eye  has  to  look  pretty  carefully  to 
see  the  smaller  star.  Yet  another  pair  is  s  Lyrse,  the  com- 
ponents of  which  are  so  close  that  only  a  good  eye  can  dis- 
tinguish them.  These  paii-s,  however,  are  not  considered  as 
double  stars  in  astronomy,  because,  although  to  the  naked  eye 
they  seem  so  close,  yet,  when  viewed  in  a  telescope  of  high 
power,  they  are  so  wide  apart  that  they  cannot  be  seen  at  the 
same  time.  The  telescopic  double  stars  are  formed  of  com- 
ponents only  a  few  seconds  apart ;  indeed,  in  man\-  cases,  only 
a  fraction  of  a  second.  The  large  majority  of  those  which 
are  catalogued  as  doubles  range  from  half  a  second  to  fifteen 
seconds  in  distance.  When  they  exceed  the  latter  limit,  they 
are  no  longer  objects  of  special  interest,  because  they  may 
be  really  without  any  connection,  and  appear  together  only 
because  they  lie  in  nearly  the  same  straight  line  from  our 
system. 

Tlio  most  obvious  question  which  suggests  itself  here  is 
whether  in  any  case  there  is  any  real  connection  between  the 
two  stars  of  the  pair,  or  whether  they  do  not  appear  close  to- 
gethePj  simply  because  they  chance  to  lie  on  nearly  the  same 


DOUBLE  STARS.  449 

straight  line  from  the  earth.  That  some  stare  do  appear  dou- 
ble in  this  way  there  is  no  doubt,  and  such  pairs  are  called 
"optically  double."  But  notwithstanding  the  innnense  num- 
ber of  visible  stars,  the  chance  of  many  pairs  falling  within 
a  few  seconds  of  each  other  is  quite  small ;  and  the  number 
of  close  double  stars  is  so  great  as  to  preclude  all  possibility 
that  they  appear  together  only  by  chance.  If  any  further 
proof  was  wanted  that  the  stars  of  these  pairs  are  really  phys- 
ically connected,  and  therefore  close  together  in  reality  as  well 
as  in  appearance,  it  is  found  in  the  fact  that  many  of  them 
constitute  systems  in  which  one  revolves  round  the  other,  or, 
to  speak  more  exactly,  in  which  each  revolves  round  the  cen- 
tre of  gravity  of  the  pair.  Such  pairs  are  called  hinary  sys- 
tems, to  distinguish  them  from  those  in  which  no  such  revolu- 
tion has  been  observed.  The  revolution  of  these  biuar\'  sys- 
tems is  generally  very  slow,  i-equiring  many  centr.>\es  for  its 
accomplishment ;  and  the  slower  the  motion,  the  longer  it 
will  take  to  perceive  and  determine  it.  Generally  it  has  been 
detected  by  astronomers  of  one  generation  comparing  their 
observations  with  those  of  their  predecessors  ;  for  instance, 
when  the  elder  Struve  compared  his  observations  with  those 
of  Herschel,  and  when  Dawes  or  the  younger  Struve  compared 
with  the  elder  Struve,  a  great  iiumber  of  pairs  were  found  to 
be  binary.  As  ever}"  observer  is  constantly  detecting  new 
cases  of  motion,  the  number  of  binary  systems  known  to  as- 
tronomei'S  is  constantly  increasing. 

A  brief  account  of  the  manner  in  which  these  objects  are 
measured  may  not  be  out  of  place.  For  the  purpose  in  ques- 
tion, the  eye-piece  of  the  telescope  must  be  provided  with  a 
"filar  micrometer,"  the  important  part  of  which  consists  of  a 
pair  of  parallel  spider-lines,  one  of  which  can  be  moved  side- 
ways by  a  very  fine  screw,  and  can  thus  be  made  to  pass  back 
and  forth  over  the  other.  The  exact  distance  apart  of  the 
lines  can  be  determined  from  the  position  of  the  screw.  The 
whole  micrometer  turns  round  on  an  axis  parallel  to  the  tel- 
escope, the  centre  of  which  is  in  the  centre  of  the  field  of 
viow.    To  get  the  direction  uf  one  star  from  the  other,  the  ob- 


450 


THE  STELLAR   UNIVERSE. 


server  turns  the  micrometer  round  until  tlie  spider-lines  are 
parallel  to  the  line  joining  the  two  stars,  as  shown  in  Fig.  98, 
and  he  then  reads  the  position  circle.  Knowing  what  the 
position  circle  reads  when  he  turns  the  wires  so  that  the  star 
shall  run  along  them  by  its  diurnal  motion,  the  difference  of 
the  two  angles  sliows  the  angle  which  the  line  joining  the 
two  stars  makes  with  the  celestial  parallel.  To  obtain  the 
distance  apart  of  the  stars,  the  obser\er  turns  the  micrometer 
90°  from  the  position  in  Fig.  98,  and  then  turns  the  screw  and 
moves  the  telescope,  until  each  star  is  bisected  b}'  one  of  the 
wires,  as  shown  in  Fig.  99.  The  position  of  the  wires  is  then 
interchanged,  and  the  measure  is  repeated.      The  mode  in 

N 
Ik 

I         i 


s 


Fig.  9S. 


Fig.  99. 


Fig.  100. 


which  the  direction  of  one  star  from  another  is  reckoned  is 
this:  Imagine  a  line,  SN,  in  Fig.  100,  drawn  due  north  from 
the  brighter  star,  and  another,  SP,  drawn  through  the  smaller 
star.  Then  the  angle  NSP  which  these  two  lines  make  with 
each  other,  counted  from  north  towards  east,  is  the  position 
angle  of  the  stars,  the  changes  in  which  show  the  revolution 
of  one  star  around  the  other. 

In  a  few  of  the  binary  systems  the  period  is  so  short  that 
{a  complete  revolution,  or  more,  of  the  two  stars  round  each 
other  has  been  observed.  As  a  general  rule,  the  pairs  which 
have  the  most  rapid  motion  are  very  close,  and  therefore  of 
comparatively  recent  discovery,  and  difficult  to  observe.  One 
or  two  are  suspected  to  have  a  period  of  less  than  thirty  years, 
but  tliey  are  very  hard  to  measure. 

Binary  Systems  of  Short  Period. — The  following  table  shows 


DOUBLE  STABS. 


451 


the  periods  of  revolution  in  the  case  of  those  stars  which  have 
been  observed  through  a  complete  revolution,  or  of  which  the 
periods  have  been  well  determined : 


42  Comje 26  years. 

?  Herculis 35      " 

Stnive,  3121 40      " 

ijCoionae 40      " 

Siriiis 50      " 

^Caiicri 58      " 


?  UrsjB  Majoris G3  years. 

»/ Coionse  Borealis 67      " 

a  Centauri 77      " 

/zOphiuchi 92      " 

\  Ophiuchi 96      " 

^Scorpii 98      " 


Two  or  three  others  arc  suspected  to  move  very  rapidly,  but 
they  are  so  very  close  and  difficult  that  it  is  only  on  favora- 
ble occasions  that  they  can  be  seen  to  be  double.  One  of 
the  most  remarkable  stars  in  this  list  is  Sirius,  the  period  of 
which  is  calculated,  not  from  the  observations  of  the  satel- 
lite, but  from  the  motion  of  Sirius  itself.  It  has  long  been 
known  that  the  proper  motion  of  this  star  is  subject  to  cer- 
tain periodic  variations ;  and,  on  investigating  these  varia- 
tions, it  was  found  by  Peters  and  Auwers  that  they  could  be 
completely  represented  by  supposing  that  a  satellite  was  re- 
volving around  the  planet  in  a  certain  orbrt.  The  elements 
of  this  orbit  were  all  determined  excej^t  the  distance  of  the 
satellite,  which  did  not  admit  of  determination.  Its  direction 
could,  however,  be  computed  from  time  to  time  almost  as  ac- 
curately as  if  it  were  actually  seen  with  the  telescope.  But, 
before  the  time  of  which  we  speak,  no  one  had  ever  seen  it. 
Indeed,  although  many  observers  must  have  examined  Sirius 
from  time  to  time  with  good  telescopes,  it  is  not  likely  that 
they  made  a  careful  search  in  the  predicted  direction. 

Such  was  the  state  of  the  question  until  February,  1862, 
when  Messrs.  Alvan  Clark  &  Sons,  of  Cambridgeport,  were 
completing  their  eighteen-inch  glass  for  the  Chicago  Observa- 
tory. Turning  the  glass  one  evening  on  Sirius,  for  the  pur- 
pose of  trying  it,  the  practised  eye  of  the  younger  Clark  soon 
detected  something  unusual.  "  Why,  father,"  he  exclaimed, 
"  the  star  has  a  companion  !"  The  father  looked,  and  there 
was  a  faint  companion  due  east  from  the  bright  star,  and  dis- 
tant about  10''.     This  was  exactly  the  predicted  direction  ioi 


452  THE  STELLAR   UNIVERSE. 

that  time,  though  the  discoverers  knew  nothing  of  it.  As  the 
news  went  round  the  world,  all  the  great  telescopes  were 
pointed  on  Sirius,  and  it  was  now  found  tliat  when  observere 
knew  where  the  companion  was,  many  telescopes  would  show 
it.  It  lay  in  the  exact  direction  which  theory  had  predicted 
for  that  time,  and  it  was  now  observed  with  the  greatest  inter- 
est, in  order  to  see  whether  it  was  moving  in  the  direction  of  the 
theoretical  satellite.  Four  yeai-s'  observation  showed  that  this 
was  really  the  case,  so  that  hardly  any  doubt  could  remain  that 
this  almost  invisible  object  was  really  the  body  which,  by  its  at- 
traction and  revolution  around  Sirius,  had  caused  the  inequal- 
ity in  its  motion.  At  the  same  time,  the  correspondence  has 
not  since  proved  exact,  the  observed  companion  having  moved 
about  half  a  degree  per  annum  more  rapidly  than  the  theO' 
retieal  one.  This  difference,  though  larger  than  was  expected, 
is  probably  due  to  the  inevitable  errors  of  the  very  delicate 
and  difficult  observations  from  which  the  movements  of  the 
theoretical  companion  were  computed. 

The  visibility  of  this  very  interesting  and  difficult  object 
depends  almost  as  much  on  the  altitude  of  Sirius  and  the  state 
of  the  atmosphere  as  on  the  power  of  the  telescope.  When 
the  images  of  the  stare  are  very  bad,  it  cannot  be  seen  even 
in  the  great  AVashington  telescope,  while  there  are  cases  of  its 
being  seen  under  extraordinarily  favorable  conditions  with  tel- 
escopes of  six  inches  aperture  or  less.  These  favorable  condi- 
tions are  indicated  to  the  naked  eye  by  the  absence  of  twinkling. 

A  case  of  the  same  kind,  except  that  the  disturbing  satellite 
has  not  been  seen,  is  found  in  Procyon.  Bessel  long  ago  sus- 
pected that  the  position  of  this  star  was  changed  by  some  at- 
tracting body  in  its  neighborhood,  but  he  did  not  reach  a  defi- 
nite conclusion  on  the  subject.  Auwers,  having  made  a  care- 
ful investigation  of  all  the  observations  since  the  time  of  Brad- 
lev,  found  that  the  star  moved  around  an  invisible  centre  1" 
distant,  which  was  probably  the  centre  of  gravity  of  the  star 
and  an  invisible  satellite.  This  satellite  has  been  carefully 
eearched  for  with  great  telescopes  during  the  last  few  years, 
but  without  success. 


CLUSTEES  OF  STARS.  453 

Triple  and  Multiple  Stars.  —  Besides  double  stars,  groups 
of  three  or  more  stars  are  freqnentlv  found.  Siicli  objects 
are  known  as  triple,  quadruple,  etc.  They  comuionlj'  occur 
thrcugh  one  of  the  stars  of  a  wide  pair  being  itself  a  close 
double  star,  and  very  often  the  duplicity  of  the  component 
has  not  been  discovered  till  long  after  it  was  known  to  form 
one  star  of  a  pair.  For  instauce,  fx  Ilerculis  was  recognized 
as  a  double  star  by  Sir  W.  Ilerschel,  the  companion  star  being 
about  30''  distant,  and  much  smaller  than  //  itself.  In  1856, 
Mr.  Alvau  Clark,  trying  otie  of  his  glasses  upon  it,  found  that 
the  small  companion  was  itself  double,  being  composed  of  two 
nearly  equal  stars,  about  1"  apart.  This  close  pair  proves  to 
be  a  binary  system  of  short  period,  more  than  half  a  revolu- 
tion of  the  two  stars  around  each  other  having  been  made 
since  1856.  Another  case  of  the  same  kind  is  y  Andromedie, 
which  was  found  by  Ilerschel  to  have  a  companion  about  10" 
distant,  while  Struve  found  this  companion  to  be  itself  double. 

Many  double  and  multiple  stars  are  interesting  objects  for 
telescopic  examination.  We  give  in  the  Appendix  a  list  of 
the  more  interesting  or  remarkable  of  them. 

§  5.  Clusters  of  Stars. 

A  very  little  observation  with  the  telescope  will  show  that 
while  the  bi'ighter  stars  are  scattered  nearly  equally  over  the 
whole  celestial  vault,  this  is  not  the  case  with  the  smaller  ones. 
A  number  of  stars  which  it  is  not  possible  to  estimate  are 
found  to  be  aggregated  into  clusters,  in  which  the  separate 
stars  are  so  small  and  so  numerous  that,  with  insufficient  tele- 
scopic power,  they  pre:>ent  the  appearance  of  a  mass  of  cloudy 
light.  We  find  clusters  of  every  degree  of  aggregation.  At 
one  extreme  we  may  place  the  Pleiades,  or  "seven  stars'" 
which  form  so  well-known  an  object  in  our  winter  sky,  in 
which,  however,  only  six  of  the  stars  are  plainly  visible  to  the 
naked  eye.  There  is  an  old  mytli  that  this  grou))  origiiuiUy 
consisted  of  seven  stars,  one  of  which  disappeared  from  the 
heavens,  leaving  but  six.  But  a  \ery  good  eye  can  even  now 
see  eleven  when  the  air  is  clear,  and  the  telescope  shows  fron.'. 


454  THE  STELLAR   VSIVERSE. 

tiftv  to  a  huiulred  moi-o,  according  to  its  power.    We  present  a 
view  of  this  group  as  it  appears  through  a  small  telescope. 

Mo  absolute  dividiug-liiie  can  be  drawn  between  such  wide- 
\y  extended  groups  as  the  Pleiades  and  the  densest  clusters, 


Fm.  101. —Telescopic  view  of  the  Pleiades,  after  Enpelraann.  The  elx  lnr<2:er  stars  are  thoM 
easily  seen  by  ordinary  eyes  without  a  telescope,  while  the  four  next  in  size,  having 
four  rays  each,  can  be  seen  by  very  good  eyes.  About  an  inch  from  the  upper  rlsjht' 
band  corner  is  a  pair  of  small  stars  which  a  very  keen  eye  can  see  as  a  single  star. 

The  cluster  Prissepe,  in  the  constellation  Cancer  (Map  III., 
riglit  ascension,  8  houi*8  20  minutes;  declination,  20°  10'  N.), 
is  ])lainly  visible  to  the  naked  e3'e  on  a  (;lear,  moonless  night, 
as  a,  pebnlous  mass  of  liglit    Examined  Nvith  a  small  teio* 


CLUSTERS  OF  STARS.  4o5 

scope,  it  is  found  to  consist  of  a  group  of  stars,  ranging  fi-orn 
the  seventh  or  eighth  magnitude  upwards.  For  examination 
with  a  small  telescope,  one  of  the  most  beautiful  groups  is  in 
the  constellation  Perseus  (Map  I.,  right  ascension,  2  houi's  10 
minutes ;  declination,  57°  N.),  It  is  seen  to  the  best  advantage 
with  a  low  magnifying  power,  between  twenty-tive  and  iifty 
times,  and  may  easily  be  recognized  by  the  naked  eye  as  a 
little  patch  of  light. 

The  heavens  afford  no  objects  of  more  interest  to  the  con- 
templative mind  than  some  of  these  clusters.  Maiiy  of  them 
are  so  distant  that  the  most  powerful  telescopes  ever  made 
show  thcra  only  as  a  patch  of  star-dust,  or  a  mass  of  light  so 
faint  that  the  separate  stai's  cannot  be  distinguished.  Their 
distance  from  ns  is  such  that  they  are  beyond,  not  only  all 
our  means  of  measui-ement,  bnt  all  our  powers  of  estimation. 
Minute  as  they  a[»pear,  there  is  nothing  that  we  know  of  to 
prevent  our  supposing  each  of  them  to  be  the  centre  of  a 
group  of  planets  as  extensive  as  our  own,  and  each  planet  to 
be  as  full  of  inliabitants  as  this  one.  We  may  thus  think  of 
them  as  little  colonies  on  the  outskirts  of  creation  itself,  and 
as  we  see  all  the  suns  which  give  them  light  condensed  into 
one  little  speck,  we  might  be  led  to  think  of  the  inhabitants 
of  the  various  systems  as  holding  intercourse  witli  each  other. 
Yet,  were  we  transported  to  one  of  these  distant  clusters,  and 
stationed  on  a  planet  circling  one  of  the  suns  which  compose 
it,  instead  of  finding  the  neighboring  suns  in  close  proxijnity, 
we  should  only  see  a  firmament  of  stars  around  us,  such  as  we 
see  from  the  earth.  Probably  it  Vv^ould  be  a  brighter  firma- 
ment, in  which  so  many  stars  would  glow  with  more  than  the 
splendor  of  Sirius,  as  to  make  the  night  far  brighter  than 
ours;  but  the  inhabitants  of  the  neighboring  worlds  would  as 
completely  elude  teles(!opic  vision  as  the  inhabitants  of  Mars 
do  here.  Consequently,  to  the  inhabitants  of  every  planet  in 
the  cluster,  the  question  of  the  plurality  of  worlds  might  be 
as  insolvable  as  it  is  to  us. 

To  give  the  reader  an  idea  M-hat  the  more  distant  of  these 
star  clusters  looks  like,  we  present  two  views  from  Sir  John 


456 


THE  STELLAR   UNIVERSE. 


Hersehel's  observations  at  the  Cape  of  Good  Hope.  Fig.  102 
shows  the  duster  numbered  2322  in  Hei*schel's  catalogue,  and 
known  as  47  Toucani.  That  astronomer  describes  it  as  ''a 
most  glorious  globular  cluster,  the  stars  of  the  fourteenth  mag- 
nitude itnmsnsely  numerous.  It  is  compressed  to  a  blaze  of 
light  at  the  centre,  the  diameter  of  the  more  compi'cssed  part 
being  30"  in  right  ascension."  Fig.  103  is  Xo.  3504  of  Her- 
schel :  "  The  noble  globular  cluster  tu  Centauri,  beyond  all 
comparison  the  richest  and  largest  object  of  the  kind  in  the 
heavens.      The  stars  are  literally  innumerable,  and  as  their 


Fis.  102.— Cluster  47  Toucani.   Right  ascen- 
sion, 0  hours  IS  minutes ;   declination. 


Fig.  103.— Cluster  w  Centauri.    Risht  ascen- 
sion, 13  hours  20  minutes ;   decliuation, 


72°  45'  S.  46°  52'  S. 

total  light  when  received  by  the  naked  eye  affects  it  hardly 
more  than  a  star  of  the  fifth  or  fourth  to  fifth  magnitude,  the 
minuteness  of  each  star  may  be  imagined." 

§  6.  Xehuloe. 

Nebnlse  appear  to  ns  as  masses  of  soft  diffused  light,  of 
g^reater  or  less  extent.  Generally  these  masses  are  very  ir- 
regular in  outline,  but  a  few  of  them  are  round  and  well- 
defined.  These  are  termed  jilanetary  nebulx.  It  may  some- 
times be  impo6sii)le  to  distinguish  between  star  clusters  and 
nebulae,  because  when  the  power  of  the  telescope  is  so  low 
that  the  separate  stars  of  a  cluster  cannot  be  flistinguished, 
they  will  present  the  appearancte  of  a  nebula.  T<>  tiie  naked 
eye  the  cluster  Prsesepe,  described  in  the  last  chapter,  looks 


NEBULA.  457 

exactly  like  a  nebula,  though  a  very  small  telescope  will  re- 
solve it  into  stars.  The  early  observers  with  telescopes  de- 
scribed many  objects  as  nebulae  which  the  more  powerful  in- 
struments of  Herschel  showed  to  be  clusters  of  stars.  Thus 
arose  the  two  classes  of  resolvable  and  irresolvable  nebulae, 
the  first  comprising  such  as  could  be  resolved  into  stars,  and 
the  second  such  as  could  not.  It  is  evident,  from  what  we 
have  just  said,  that  this  distinction  would  depend  partly  on 
the  telescope,  since  a  nebula  wliich  was  irresolvable  in  one 
telescope  might  be  resolvable  in  another  telescope  of  greater 
power.  This  suggests  the  question  whether  all  nebulaj  may 
not  really  be  clusters  of  stars,  those  which  are  iri-esolvable  ap- 
pearing so  merely  because  their  distance  is  so  great  that  the 
separate  stars  Avhich  compose  them  cannot  be  distinguished 
with  our  most  powerful  telescopes.  If  this  were  so,  there 
would  be  no  such  thing  as  a  real  nebula,  and  everj^thing 
which  appears  as  such  should  be  classified  as  a  star  cluster. 
The  spectroscope,  as  we  shall  presently  show,  has  settled  this 
question,  by  showing  that  many  of  these  objects  are  immense 
masses  of  glowing  gas,  and  therefore  cannot  be  stars. 

Classification  and  Forms  of  Nebuke. — The  one  object  of  this 
class  which,  more  than  all  others,  has  occupied  the  attention 
of  astronomers  and  excited  the  wonder  of  observers,  is  the 
great  nebula  of  Orion.  It  surrounds  the  middle  of  the  three 
stars  which  form  the  sword  of  Orion.  Its  position  may  be 
found  on  Maps  II.  and  III.,  in  right  ascension  5  hours  28 
minutes,  declination  6°  S.  A  good  eye  will  perceive  that 
this  star,  instead  of  looking  like  a  bright  point,  as  the  other 
stars  do,  has  an  ill-defined,  hazy  appearance,  due  to  the  sur- 
rounding nebulse.  This  object  was  fii-st  described  by  Huy- 
ghens  in  1659,  as  follows  : 

"  There  is  one  phenomenon  among  the  fixed  stai*s  worthy 
of  mention  which,  so  far  as  I  know,  has  hitherto  been  noticed 
by  no  one,  and  indeed  caimot  be  well  observed  except  with 
large  telescopes.  In  tlie  sword  of  Orion  are  three  stars  quite 
close  together.  In  1656,  as  I  chanced  to  be  viewing  the  mid- 
dle one  of  these  with  the  telescope,  instead  of  a  single  star, 


i5S 


THE  STELLAR    VXIVEESE. 


twelve  showed  themselves  (a  not  uncommon  circumstance). 
Three  of  these  almost  touched  each  other,  and,  with  four  oth- 
ers, shone  through  a  nebula,  so  that  the  space  around  them 
seemed  far  brighter  than  the  rest  of  the  heavens,  which  was 
entirely  clear,  and  appeared  quite  black,  the  effect  being  that 
of  an  opening  in  the  sky,  through  which  a  brighter  region 
was  visible.'"'^ 


Fig.  104.— The  great  nebn'.a  of  Orion,  as  drawn  by  Troavelot  with  the  tweuty-sLx-inch 
Washington  telescope. 

Since  that  time  it  has  been  studied  with  large  telescopes 
b}'  a  great  number  of  observere,  including  Messier,  the  two 


*  Systerna  Saturnium.  p.  S.  The  last  remark  of  Huyghens  seems  to  have  pro- 
duced the  impression  that  he  or  some  of  the  early  obser^•er8  considered  the  nebulae 
to  be  real  openings  in  the  firmament,  through  which  they  got  glimpses  of  the 
glory  of  the  empyrean.  But  it  may  be  doubted  whether  the  old  ideas  of  the  firma- 
ment and  the  empyrean  were  entertained  by  any  astronomer  after  the  invention 
of  the  telescope,  and  there  is  nothing  in  the  remark  of  Huygliens  to  indicate  that 
he  thought  the  opening  really  exisf^d.     His  words  are  rather  obscure. 


NEBULA.  459 

Herschels,  Rosse,  Struve,  and  the  Bonds.  The  representatiun 
which  we  give  in  Fig.  104  is  from  a  drawing  made  bj  Mr. 
Trouvelot  with  the  great  Washington  telescope.  In  brilHancy 
and  variety  of  detail  it  exceeds  any  other  nebula  visible  in 
the  northern  hemisphere.  The  central  point  of  interest  is  oc- 
cupied by  four  comparatively  bright  stars,  easily  distinguished 
by  a  small  telescope  with  a  magnifying  power  of  40  or  50, 
combined  with  two  small  ones,  requiring  a  nine-inch  telescope 
to  be  well  seen.  The  whole  of  these  form  a  sextuple  group, 
included  in  a  space  a  few  seconds  square,  which  alone  would 
be  an  interesting  and  remarkable  object.  Besides  tliese,  the 
nebula  is  dotted  with  so  many  stars  that  they  would  almost 
constitute  a  cluster  by  themselves. 

In  the  winter  of  1864-65,  the  spectrum  of  this  object  was 
examined  independently  by  Secchi  and  Iluggins,  who  found 
that  it  consisted  of  three  bright  lines,  and  hence  concluded 
that  the  nebula  was  composed,  not  of  stars,  but  of  glowing 
gas.  The  position  of  one  of  the  lines  was  near  that  of  a  line 
of  nitrogen,  while  another  seemed  to  coincide  with  a  hydrogen 
line.  There  is,  therefore,  a  certain  probability  that  this  object 
is  a  mixture  of  hydrogen  and  nitrogen  gas,  though  this  is  a 
point  on  which  it  is  iuipossible  to  speak  with  certainty. 

Another  brilliant  nebula  visible  to  the  naked  eye  is  the 
great  one  of  Andromeda  (Maps  II.  and  V.,  i-ight  ascension, 
0  hours  35  minutes;  declination,  40°  N.).  Tlie  observer  can 
see  at  a  glance  witii  the  naked  eye  that  this  is  iK»t  a  star,  but 
a  mass  of  diffused  light.  Indeed,  untrained  observers  liave 
sometimes  very  naturally  mistaken  it  for  a  comet.*  It  was 
first  described  by  Marius,  in  1614,  who  compared  its  light  to 
that  of  a  candle  shining  through  horn.  This  gives  a  very 
good  idea  of  the  singular  impression  it  produces,  which  is  that 
of  an  object  not  self-luminous,  but  translucent,  and  illuminated 
by  a  very  brilliant  light  behind  it.     With  a  small  telescope,  it 

*  A  ship-captain  who  had  crossed  the  Atlantic  once  visited  the  Cambridge  Oh- 
seiTatory,  to  tell  Professor  Bond  that  he  iiad  seen  a  small  comet,  which  remained 
in  sight  during  his  entire  voyage.  The  object  proved  to  be  the  nebula  oC  An- 
dromeda. 


4:60  THE  STELLAR   UNIVERSE. 

is  easy  to  imagine  it  to  be  a  solid  like  horn ;  but  with  a  large 
one,  the  effect  is  much  more  tliat  of  a  great  mass  of  matter, 
like  fog  or  mist^  which  scatters  and  reflects  the  light  of  a  brill- 
iant body  in  its  midst.  That  this  impression  can  be  correct, 
it  would  be  hazardous  to  assert ;  but  the  result  of  a  spectrum! 


Fio.  105.— The  anuuhir  nebula  iu  Lyra.     Drawn  by  Professor  E.  S.  Holdeo. 

analysis  of  the  light  of  tlie  nebula  certainly  seems  to  favor  it 
Unlike  most  of  the  uebulfe,  its  spectrum  is  a  continuous  one, 
similar  to  the  ordinarj'  spectra  from  lieated  bodies,  thus  indi- 
cating that  the  light  emanates,  not  from  a  glowing  gas,  but 
from  matter  in  the  solid  or  liquid  state.     This  would  suggest 


NEBULA.  461 

the  idea  that  the  object  is  really  an  immense  star- cluster,  so 
distant  that  the  most  powerful  telescopes  cannot  resolve  it. 
Though  we  cannot  positively  deny  the  possibility  of  this,  yet 
in  tlie  most  powerful  telescopes  the  light  fades  away  so  softly 
and  gradually  that  no  such  thing  as  a  resolution  into  stars 
seems  possible.  Indeed,  it  looks  less  resolvable  and  more  like 
a  gas  in  the  largest  telescopes  than  in  those  of  moderate  size. 
If  it  is  really  a  gas,  and  if  the  spectrum  is  continuous  through- 
out the  whole  extent  of  the  nebula,  it  would  indicate  either 
that  it  shone  by  reflected  light,  or  that  the  gas  was  subjected 
to  a  great  pressure  almost  to  its  outer  limit,  which  hardly  seems 
possible.  But,  granting  that  the  light  is  reflected,  we  cannot 
say  whether  it  originates  in  a  single  bright  star  or  in  a  num- 
ber of  small  ones  scattered  about  through  the  nebula. 

Another  extraordinary  object  of  this  class  is  the  annular,  or 
ring-nebula  of  Lyra,  situated  in  that  constellation,  about  half- 
way between  the  stars  /3  and  j.  In  the  older  telescopes  it 
looked  like  a  perfect  ring;  but  the  larger  ones  of  modern  times 
show  that  the  opening  of  the  ring  is  really  filled  with  nebu- 
lous light ;  in  fact,  that  we  have  here  an  object  of  very  regular 
outline,  in  which  the  outer  portion  is  brighter  than  the  inte- 
rior. Its  form  is  neither  circular  nor  exactly  elliptic,  but  egg- 
shaped,  one  end  being  more  pointed  than  the  other.  A  mod- 
erate-sized telescope  will  show  it,  but  a  large  one  is  required 
to  see  it  to  good  advantage. 

It  would  appear,  from  a  comparison  of  drawings  made  at 
different  dates,  that  some  nebulae  are  subject  to  gi-eat  changes 
of  for)n.  Especially  does  this  hold  true  of  the  nebula  sur- 
rounding the  remarkable  variable  star  7;  Argus.  In  many 
other  nebulee  changes  have  been  suspected ;  but  the  softness 
and  indistinctness  of  outline  which  characterize  most  of  these 
objects,  and  the  great  difference  of  their  aspect  when  seen  in 
telescopes  of  very  different  powers,  make  it  difficult  to  prove  a 
change  from  mere  differences  of  drawino:.  One  of  the  stronc'- 
est  cases  in  favor  of  change  has  been  made  out  by  Professor 
Holden  frotn  a  study  of  drawings  and  descriptions  of  what  is 
called  the  "  Omega  nebula,"  from  a  resemblance  of  one  of 


462 


THE  STELLAR   UNIVERSE. 


Fig.  106.— The  Omega  nebula ;  Herschel  2008.     Right  ascension,  IS  houre  13  miuntes ; 
declination,  16"  U'  S.    After  Holden  and  Trouvelot. 

its  branches  to  the  Greek  letter  Q.  We  present  a  figure  of 
this  object  as  it  now  appeai-s,  from  a  diawiiig  by  Pi-ofessor 
Holden  and  Mr.  Trouvelot,  witli  the  great  Washington  tele- 
scope. It  is  the  branch  on  the  left-hand  end  of  the  nebula 
which  was  formerly  supposed  to  have  the  form  of  Q. 

As  illustrative  of  the  fantastic  forms  which  nebulae  some- 
times assume,  we  present  Ilerschers  views  of  two  more  neb- 
ulie.  That  shown  in  Fig.  1<'»S  he  calls  the  "looped  nebula," 
and  describes  as  one  of  the  most  extraordinary  objects  in  the 
heavens.  It  cannot  be  seen  to  advantage  except  in  the  south- 
ern hemisphere. 

Distribution  of  the  Nebub.p.  —  A  remarkable  feature  of  the 
distribution  of  the  ncbulie  is  that  they  are  most  numerous 
where  the  stars  arc  least  so.  While  the  stai"S  grow  thicker  as 
we  approach  the  region  of  the  Milky  Way,  the  nebulae  dimin- 
ish in  number.     Sir  John  Herschel  remarks  that  one-third  of 


NEBULA. 


4G3 


Fio.  107.— Nebnla  Herschel  3722.    Eight  ascension,  17  hours  56  miuutes ;  declination,  24* 
21'  S.    After  Sir  John  Herschel. 

the  nebulous  contents  of  the  heavens  are  congregated  in  a 
broad,  irregular  patch  occupying  about  one -eighth  the  sur- 
face of  the  celestial  sphere,  extending  from  Ui-sa  Major  in  the 
north  to  Yirgo  in  the  south.  If,  however,  we  consider,  not  the 
true  nebulae,  but  star  clusters,  we  lind  the  same  tendenc}'  to 
condensation  in  the  Milky  Way  that  we  do  in  the  stars.  We 
thus  have  a  clearly  marked  dis- 
tinction between  nebulae  and 
stars  as  regards  the  law  of  their 
distribution.  The  law  in  ques- 
tion can  be  most  easily  under- 
stood by  the  non-mathematical 
reader  by  supposing  the  starry 
sphere  in  such  a  position  that 
the  Milky  Way  coincides  with 
the  horizon.  Then  the  stars  and 
star  clusters  will  be  fewest  at  the 
zenith,  and  will  increase  in  number  as  we  approach  the  horizon. 
Also,  in  the  invisible  hemisphere  the  same  law  will  hold,  tlie 
stars  and  clusters  being  fewest  under  our  feet,  and  will  increase 
as  we  approach  the  horizon.  But  the  true  nebulas  will  then 
X  31 


Fio.  lOS.— The  looped  nebnla  ;  Herschel 
2941.  Right  ascension,  5  hours  40  miu- 
utes ;  decliaatiou,  69°  6'  S. 


464  TEE  STELLAR   UNIVERSE. 

be  fewest  in  the  horizon,  and  will  increase  in  number  as  we  ap- 
proach the  zenith,  or  as,  going  below  the  horizon,  we  approach 
the  nadir.  The  positions  of  the  nebulae  and  clusters  in  Sir  John 
Herschel's  great  catalogue  have  been  studied  by  Mr.  Cleve- 
land Abbe  with  especial  reference  to  their  distance  from  the 
galactic  circle,  and  the  following  numbei'S  show  part  of  his  re- 
sults. Imagine  a  belt  thirty  degrees  wide  extending  around 
the  heavens,  including  the  Milky  Way,  and  reaching  fifteen 
degrees  on  each  side  of  the  central  circle  of  the  Milky  Way. 
This  belt  will  include  nearly  one-fourth  the  surface  of  the  ce- 
lestial sphere,  and  if  the  stai-s  or  nebulae  were  equally  distrib- 
uted, nearly  one-fourth  of  them  would  be  found  in  the  belt. 
Instead,  however,  of  one-fourth,  we  find  nine-tenths  of  the  star 
clustei-s,  but  only  one-tenth  of  the  nebulae. 

The  discovery  that  the  nebulae  are  probably  masses  of  glow- 
ing gas  is  of  capital  importance  as  tending  to  substantiate  the 
view  of  Sir  William  Herschel,  that  these  masses  are  the  crude 
material  out  of  which  suns  and  systems  are  forming.  This 
view  was  necessarily  an  almost  purely  speculative  one  on  the 
part  of  that  distinguished  astronomer ;  but  unless  Me  suppose 
that  the  nebula?  are  objects  of  almost  miraculous  power,  there 
must  be  some  truth  in  it.  A  nebulous  body,  in  order  to  shine 
by  its  own  light,  as  it  does,  must  be  hot,  and  must  be  losing 
heat  through  the  vei*y  radiation  by  which  we  see  it.  As  it 
cools,  it  must  contract,  and  this  contraction  cannot  cease  un- 
til it  becomes  either  a  solid  body  or  a  system  of  such  bodies 
revolving  round  each  other.  We  shall  explain  this  more  fully 
in  treating  of  cosmical  physics  and  the  nebular  hypothesis. 

§  7.  Proper  Motions  of  the  Stars. 

To  the  unassisted  eye,  the  stare  seem  to  preserve  the  same 
relative  positions  in  the  celestial  sphere  generation  after  gen- 
eration. If  Job,  Hipparchus,  or  Ptolemy  should  again  look 
upon  the  heavens,  he  would,  to  alV  appearance,  see  Aldebaran, 
Orion,  and  the  Pleiades  exactly  as  he  saw  tliem  tliousands  of 
yeai*s  ago,  without  a  single  star  being  moved  from  its  place. 
But  the  refined  methods  of  modern  astronomy,  in  Avhich  the 


PROPER  MOTIONS  OF  THE  STARS.  465 

telescope  is  brought  in  to  measure  spaces  absolutely  invisible 
to  the  eye,  have  shown  that  this  seeming  unchangeability  is 
not  real,  and  that  the  stars  are  actually  in  motion,  only  the 
rate  of  change  is  so  slow  that  the  eye  would  not,  in  most  cases, 
notice  it  for  thousands  of  years.  In  ten  thousand  years  quite 
a  number  of  stars,  especially  the  brighter  ones,  would  be  seen 
to  have  moved,  while  it  would  take  a  hundred  thousand  years 
to  introduce  a  very  noticeable  change  in  the  aspect  of  the  con- 
stellations. 

As  a  general  rule,  the  brighter  stars  have  the  greatest 
proper  motions.  But  this  is  a  rule  to  which  there  are  many 
exceptions.  The  star  which,  so  far  as  known,  has  the  greatest 
proper  motion  of  all — namely,  Groombridge  1830 — is  of  the 
seventh  magnitude  only.  Next  in  the  order  of  proper  motion 
come  Dr.  Gould's  star,  Lacaille  9352,  of  the  seventli  magnitude, 
and  the  pair  of  stars  61  Cygni,  of  the  sixth  magnitude.  Kext 
are  four  or  five  others,  of  the  fourth  and  fifth  magnitudes. 
The  annual  motions  of  these  stars  are  as  follows : 


Groombridge  1830 7".0 

Lacaille  9352  (Gould) ....  6".2 

61  Cygni 5".2 

Lalande  21186 4".  7 


c  Indi 4".  5 

Lalande  21258 4".4 

o"  Eridani 4".l 

fi  Cassiopeiae 3".8 


The  first  of  these  stars,  though  it  has  the  greatest  proper 
motion  of  all,  would  require  185,000  years  to  perform  the 
circuit  of  the  heavens,  while  //  Cassiopeise  would  require  near- 
ly 340,000  years  to  perform  the  same  circuit.  Slow  as  these 
motions  are,  they  are  very  large  compared  with  those  of  most 
of  the  stars  of  corresponding  magnitude.  As  a  general  rule, 
the  stars  of  the  fourth,  fifth,  and  sixth  magnitudes  move  only 
a  few  seconds  in  a  hundred  years,  and  would  therefore  re- 
quire many  millions  of  years  to  perform  the  circuit  of  the 
heavens. 

So  far  as  they  have  yet  been  observed,  and,  indeed,  so  far 
as  they  can  be  observed  for  many  centuries  to  come,  these 
motions  take  place  in  perfectly  straight  lines.  If  each  star  is 
moving  in  some  orbit,  the  orbit  is  so  immense  that  no  curva- 
ture can  be  perceived  in  the  short  arc  which  has  been  de- 


4G6  THE  STELLAR  UNIVERSE. 

scribed  since  accurate  determinations  of  the  positions  of  the 
stare  be^an  to  be  made.  So  far  as  mere  observation  can  in- 
foi-m  us,  there  is  no  reason  to  suppose  that  the  stars  ai-e  sever- 
ally moving  in  definite  orbits  of  any  kind.  It  is  true  that 
Miidler  attempted  to  show,  from  an  examination  of  the  proper 
motions  of  the  stars,  that  the  whole  stellar  univei-se  was  revolv- 
ing around  the  star  Alcyone,  of  the  Pleiades,  as  a  centre — a 
theory  the  grandeur  of  wliich  led  to  its  wide  diffusion  in  popu- 
lar writings.  But  not  the  slightest  weight  has  ever  been  given 
it  by  astronomei-s,  who  have  always  seen  it  to  be  an  entirely 
baseless  speculation.  If  the  stars  were  moving  in  any  regular 
circular  orbits  whatever  having  a  common  centre,  we  could 
trace  some  regularity  among  their  proper  motions.  But  no 
such  regularity  can  be  seen.  The  stars  in  all  parts  of  the 
heavens  move  in  all  directions,  with  all  sorts  of  velocities.  It 
is  true  that,  by  averaging  the  proper  motions,  as  it  were,  we 
can  trace  a  certain  law  in  them  ;  but  this  law  indicates,  not  a 
particular  kind  of  orbit,  but  only  an  apparent  proper  motion, 
common  to  all  the  stars,  which  is  probably  due  to  a  real  mo- 
tion of  our  sun  and  solar  system. 

The  Solar  Motion. — As  our  sun  is  merely  one  of  the  stars, 
and  rather  a  small  star  too,  it  may  have  a  proper  motion  as 
well  as  the  other  stai-s.  Moreover,  when  Ave  speak  of  the 
proper  motion  of  a  star,  we  mean,  not  its  absolute  motion,  but 
only  its  motion  relative  to  our  system.  As  the  sun  moves,  he 
carries  the  earth  and  all  the  planets  along  with  him ;  and  if 
we  observe  a  star  at  perfect  rest  while  we  ourselves  are  thus 
moving,  the  star  will  appear  to  move  in  the  opposite  direc- 
tion, as  we  have  alread\'  shown  in  explaining  the  Copernican 
system.  Hence,  from  an  observation  of  the  motion  of  a  sin- 
gle star,  it  is  impossible  to  decide  how  much  of  this  apparent 
motion  is  due  to  the  motion  of  our  system,  and  how  much  to 
the  real  motion  of  the  star.  If,  however,  we  should  observe  a 
great  number  of  stars  on  all  sides  of  us,  and  find  them  all  ap- 
parently moving  in  the  same  direction,  it  would  be  natural  to 
conclude  that  it  was  really  our  system  which  was  moving,  and 
not  the  stars.     Now,  when  Herschel  averaged  the  proper  mo* 


PBOPER   MOTIONS  OF  THE  STABS.  467 

tions  of  the  stars  in  different  regions  of  the  heavens,  he  found 
that  this  was  actually  the  case.  In  general,  the  stars  moved 
from  the  direction  of  the  constellation  Hercules,  and  towards 
the  opposite  point  of  the  celestial  sphere,  near  the  constella- 
tion Argus.  This  would  show  that,  relatively  to  the  general 
mass  of  the  stars,  our  sun  was  moving  in  the  direction  of  the 
constellation  Hercules.  Herschel's  data  for  this  conclusion 
were,  necessarily,  rather  slender.  The  subject  was  afterwards 
very  carefully  investigated  by  Argelander,  and  then  by  a  num- 
ber of  other  astronomers,  whose  results  for  the  point  of  the 
heavens  towards  which  the  sun  is  moving  are  as  follows: 


Argelander 

O.  Struve 

Lundahl 

Galloway 

M&dler  " 

Airy  and  Dunkin. 


Right  Ascension. 

Declination. 

257°  49' 

28°  50'  N. 

261°  22' 

37°  36'  N. 

252°  24' 

14°  26'  N. 

260°     1' 

34°  23'  N. 

261°  88' 

39°  54'  N. 

262°  29' 

28°  58'  N. 

It  will  be  seen  that  while  there  is  a  pretty  wide  range  among 
the  authorities  as  to  the  exact  point,  and,  therefore,  some  un- 
certainty as  to  where  we  should  locate  it,  yet,  if  we  lay  the 
different  points  down  on  a  star-map,  we  shall  find  that  they 
all  fall  in  the  constellation  Plercules,  which  was  originally  as- 
signed by  Herschel  as  that  towards  which  we  wei-e  moving. 

As  to  the  amount  of  the  motion,  Struve  found  that  if  the 
sun  were  viewed  from  the  distance  of  an  average  star  of  the 
first  magnitude  placed  in  a  direction  from  us  at  right  angles 
to  that  of  the  solar  motion,  it  would  appear  to  move  at  the 
rate  of  33".9  per  century.  Dunkin  found  the  same  motion  to 
be  33".5  or  4cl'\0,  according  to  the  use  he  made  of  stars  hav- 
ing large  proper  motions. 

Motion  of  Groups  of  Stars. — There  are  in  the  heavens  sev- 
eral cases  of  widely  extended  groups  of  stains,  having  a  com- 
mon proper  motion  entirely  different  from  that  of  the  stars 
around  and  among  them.  Such  groups  must  form  connected 
systems,  in  the  motion  of  which  all  the  stars  are  carried  along 
together  without  any  great  change  in  their  positions  relative 


468  TRE  STELLAR   UNIVERSE. 

to  each  other.  The  most  remarkable  case  of  this  kind  oc- 
curs in  the  constellation  Taurus.  A  large  majority  of  the 
brisrhter  stars  in  the  resrion  between  Aldebaran  and  the  Plei- 
ades  have  a  common  proper  motion  of  about  ten  seconds  per 
century  towards  the  east.  How  many  stars  are  included  in 
this  group  no  one  knows,  as  the  motions  of  the  brighter  ones 
only  have  been  accurately  investigated.  Mr.  R.  A.  Proctor 
has  shown  that  five  out  of  the  seven  stars  which  form  the 
Dipper,  or  Great  Bear,  are  similarly  connected.  He  proposes 
for  this  community  of  proper  motions  in  certain  regions  the 
name  of  Siar-drifl.  Besides  those  we  have  mentioned,  there 
are  cases  of  close  groups  of  stars,  like  the  Pleiades,  and  of 
pairs  of  widely  separated  stars,  in  which  star -drift  has  been 
noticed. 

Motion  in  the  Line  of  Sight. — Until  quite  recently,  the  only 
way  in  which  the  proper  motion  of  a  star  could  be  detected 
was  by  observing  its  change  of  direction,  or  the  change  of  the 
point  in  which  it  is  seen  on  the  celestial  sphere.  It  is,  how- 
ever, impossible  in  this  way  to  decide  whether  the  star  is  or  is 
not  changing  its  distance  from  our  system.  If  it  be  moving 
directly  towards  us,  or  directly  away  from  us,  we  could  not 
see  any  motion  at  all.  The  complete  motion  of  the  stars  can- 
not, therefore,  be  determined  by  mere  telescopic  observations. 
But  there  is  an  ingenious  method,  founded  on  the  undulatory 
theory  of  light,  by  which  this  motion  may  be  detected  with 
more  or  less  probability  by  means  of  the  spectroscope,  and 
which  was  first  successfully  applied  by  Mr.  Huggins,  of  Eng- 
land. According  to  the  usual  theory  of  light,  the  luminosity 
of  a  heated  body  is  a  result  of  the  vibrations  communicated 
by  it  to  the  ethereal  medium  which  fills  all  space  ;  and  if  the 
body  be  gaseous,  it  is  supposed  that  a  molecule  of  the  gas  vi- 
brates at  a  certain  definite  rate,  and  thus  communicates  only 
certain  definite  vibrations  to  the  ether.  The  rate  of  vibration 
is  determined  by  the  position  of  the  bright  line  in  the  spec- 
trum of  the  gas.  Xow,  if  the  vibrating  body  be  moving 
through  the  ether,  the  light-waves  which  it  throws  behind  it 
will  be  longer,  and  those  which  It  throws  in  front  of  it  will  be 


PROPER  MOTIONS  OF  THE  STARS.  469 

shorter,  than  if  the  body  were  at  rest.  The  result  will  be,  that 
in  the  former  case  the  spectral  lines  will  be  less  refrangible, 
or  nearer  the  red  end  of  the  spectrnm,  and  in  the  latter  case 
nearer  the  blue  end.  If  the  line  is  not  a  bright  one  which  the 
gas  emits,  but  the  corresponding  dark  one  which  it  has  ab- 
sorbed from  the  light  of  a  star  passing  through  it,  the  result 
will  be  the  same.  If  such  a  known  line  is  found  slightly 
nearer  the  blue  end  of  the  spectrum  than  it  should  be,  it  is 
concluded  that  the  star  from  which  it  emanates  is  approach- 
ing us,  while  in  the  contrary  case  it  is  receding  from  us. 

The  question  may  be  asked.  How  can  we  ideutif}'  a  line  as 
proceeding  from  a  gas,  unless  it  is  exactly  in  the  position  of 
the  line  due  to  that  gas  ?  How  do  we  know  but  that  it  may 
be  due  to  some  other  gas  which  emits  light  of  slightly  differ- 
ent refrangibility  ?  The  reply  to  this  must  be,  that  absolute 
certainty  on  this  point  is  not  attainable  ;  but  that,  from  the 
examination  of  a  number  of  stars,  the  probabilities  seem  large- 
ly in  favor  of  the  opinion  that  the  displaced  lines  are  really 
due  to  the  gases  near  whose  lines  they  fall.  If  the  lines  were 
always  displaced  in  one  direction,  whatever  star  was  exam- 
ined, the  conclusion  in  question  could  not  be  drawn,  because 
it  might  be  that  this  line  was  due  to  some  other  unknown  sub- 
stance. But  as  a  matter  of  fact,  when  different  stars  are  ex- 
amined, it  is  found  that  the  lines  in  question  are  sometimes 
on  one  side  of  their  normal  position  and  sometimes  on  the 
other.  This  makes  it  probable  that  they  really  all  belong  to 
one  substance,  but  are  displaced  by  some  cause,  and  the  motion 
of  the  star  is  a  cause  the  existence  of  which  is  certain,  and  the 
sufficiency  of  which  is  probable. 

Mr.  Huggins's  system  of  measurement  has  been  introduced 
by  Professor  Airy  into  the  Royal  Observatory,  Greenwich, 
where  very  careful  measures  have  been  made  dui-ing  tlie  past 
ten  years  by  Mr.  Christie  and  Mr.  Maunder.  To  show  how 
well  the  fact  of  the  motion  is  made  out,  we  give  in  the  tables 
on  the  following  page  the  results  obtained  by  Mr.  Hnggins 
and  by  the  Greenwich  observers  for  those  stars  in  which  the 
motion  is  the  largest : 


470 


THE  STELLAR   UNIVERSE. 


STARS    RECEDING    FROM    US. 


By  Mr.  HggKins. 

By  Greenwich. 

20  miles  per  sec. 
22     " 
15     " 
25     " 

15     " 

25  miles  per  sec. 

76     " 

receding. 

25  miles  per  sec. 

30     "          " 

STARS    APPROACHING    CS. 


By  Mr.  Muggins. 

By  Greenwich. 

Arcturus 

'>'>  miles  per  sec. 
.50     " 
39     " 
41)     " 
46     " 

41  miles  per  sec. 
36     '• 
41     " 

ai)proaching. 
approaching. 

a  Lvrae 

/3  Geminorum 

a  UrsjE  Majovis 

There  are  several  collateral  circumstances  which  tend  to 
confirm  these  results.  One  is  that  the  general  amount  of  mo- 
tion indicated  is,  in  a  rough  way,  about  what  we  should  expect 
the  stars  to  have,  from  their  observed  proper  motions,  com- 
bined with  their  probable  parallaxes.  Another  is  that  those 
Btars  in  the  neighborhood  of  Hercules  are  mostly  found  to  be 
approaching  the  earth,  and  those  which  lie  in  the  opposite  di- 
rection to  be  receding  from  it,  which  is  exactly  the  effect  which 
would  result  from  the  solar  motion  just  described.  Again,  the 
five  stai-s  in  the  Dipper  which  we  have  described  as  having  a 
common  proper  motion  are  also  found  to  have  a  common  mo- 
tion in  the  line  of  sight.  The  results  of  this  wonderful  and 
refined  method  of  determining  stellar  motion,  therefore,  seem 
worthy  of  being  received  with  some  confidence  so  far  as  the 
general  direction  of  the  motion  is  concerned.  But  the  dis- 
placement of  the  specti-al  lines  is  so  slight,  and  its  measure- 
ment a  matter  of  such  difiiculty  and  delicacy,  that  we  are  far 
from  being  sure  of  the  exact  numbers  of  miles  per  second 
given  by  the  observers.  The  discordances  between  the  results 
of  Greenwich  and  those  of  Mr,  Huggins  show  that  numerical 
certainty  was  not  attained. 

During  the  last  three  years,  Mr.  Keeler,  at  tlie  Lick  Obser- 
vatory, and  Dr.  Vogel,  at  Potsdam,  have  introduced  such  re- 
finements that  naotions  in  the  line  of  sio^ht  can  be  measured 


PROPER  MOTIONS  OF  THE  STARS.  47I 

within  a  fraction  of  a  mile  per  second  ;  and  the  hope  has  even 
been  expressed  that  the  velocity  of  the  earth  in  its  orbit,  and 
hence  the  solar  parallax,  might  be  determined  in  this  way. 
Dr.  Vogel's  system  consists  in  photographing  the  spectrum 
of  the  star  alongside  the  spectrum  of  the  sun,  or  of  some  known 
terrestrial  substance,  so  that  the  photographic  plate  affords 
a  permanent  record  by  which  the  displacement  of  the  lines 
produced  by  the  moving  star  may  be  measured  at  any  time. 
What  is  shown  on  tlie  plate  is  the  effect  of  the  combined  mo- 
tion of  the  star  to  or  from  the  earth,  and  of  the  earth  to  or 
from  the  star,  as  it  moves  around  the  sun.  By  observing  the 
velocities  at  different  seasons,  the  motion  of  the  earth  in  its 
orbit  is  indicated  with  a  remarkable  approach  to  precision. 

Another  remarkable  result  of  spectrum  photography  is  the 
detection  of  double  stars  so  close  that  no  telescope  could 
separate  them,  by  the  displacement  of  the  lines  produced  by 
their  orbital  motion.  The  first  discovery  of  this  sort  was 
made  by  Professor  Pickering,  in  the  cases  of  ^  Ursse  Majoris 
and  /3  Aurigse.  He  found  that,  at  certain  intervals,  the 
spectrum  of  these  stars  showed  the  lines  to  be  double,  while 
on  other  occasions  they  were  shown  single.  These  alterna- 
tions occurred  at  regular  intervals.  The  explanation  of  it  is 
this  :  We  have  here  a  double  star,  each  component  of  which 
sends  out  its  own  rays.  The  two  stars  are  revolving  around 
each  other.  When  they  are  nearly  in  the  same  line  from  the 
earth,  the  lines  formed  by  the  light  from  the  two  stars  coal- 
esce, and  seem  as  a  single  line,  but  when  one  star  is  moving 
from  the  earth,  and  the  other  moving  to  it,  the  lines  produced 
by  one  are  displaced  toward  the  red  end  of  the  spectrum,  and 
those  produced  by  the  other  toward  the  blue  end.  Thus  they 
are  separated  so  as  to  form  a  double  line. 

Dr.  Vogel  has  found  that  a  similar  phenomena  is  presented  by 
a  Virginis;  only,  instead  of  the  lines  doubling,  the  star  itself 
moves  back  and  forth  in  a  period  of  four  days.  This  shows  that 
a  comparatively  dark,  invisible  companion  is  moving  round 
it.  Thus  spectroscopic  examination  is  bringing  to  light  dark 
planets  moving  around  the  fixed  stars,  the  detection  of  which 
would  h-ave  been  forever  hopeless  by  direct  telescopic  researcli. 


472  THE  STELLAR  UNIVERSE. 


CHAPTER  n. 

THE    STRUCTTKE   OF   THE   UNIVERSE. 

Hating  in  the  preceding  chapter  described  those  features 
of  the  universe  which  the  telescope  exhibits  to  us,  we  have 
now,  in  pursuance  of  our  plan,  to  inquire  what  light  telescopic 
discoveries  can  throw  upon  the  structure  of  the  universe  as  a 
whole.  Here  we  necessarily  tread  upon  ground  less  sure  than 
that  which  has  hitheito  supported  us,  because  we  are  on  the 
very  boundaries  of  human  knowledge.  Many  of  our  conclu- 
sions must  be  more  or  less  hypothetical,  and  liable  to  be  modi- 
fied or  disproved  by  subsequent  discoveries.  We  shall  en- 
deavor to  avoid  all  mere  guesses,  and  to  state  no  conclusion 
which  has  not  some  apparent  foundation  in  observation  or 
analog}'.  The  human  mind  cannot  be  kept  from  speculating 
upon  and  wondering  about  the  order  of  creation  in  its  widest 
extent,  and  science  will  be  doing  it  a  service  in  throwing  ev- 
ery possible  light  on  its  path,  and  preventing  it  from  reaching 
any  conclusion  inconsistent  with  observed  facts. 

The  first  question  which  we  reach  in  regular  order  is,  How 
are  the  forty  or  fifty  millions  of  stars  visible  in  the  most  pow- 
erful telescopes  arranged  in  space  ?  We  know,  from  direct 
observation,  how  they  are  arranged  with  respect  to  direction 
from  our  system;  and  we  have  seen  that  the  vast  majority  of 
small  stars  visible  in  great  telescopes  are  found  in  a  belt  span- 
ning the  heavens,  and  known  as  the  Milky  "Way.  But  this 
gives  us  no  complete  information  respecting  their  absolute  po- 
sition :  to  determine  this,  we  must  know  the  distance  as  well 
as  the  direction  of  each  star.  But  beyond  the  score  or  so  of 
stars  which  have  a  measurable  parallax,  there  is  no  known 
way  of  measuring  the  stellar  distances ;  so  that  all  we  can  do 


VIEWS  OF  MODEBN  ASTRONOMERS.  473 

is  to  make  more  or  less  probable  conjectures,  founded  on  the 
apparent  magnitude  of  the  individual  stars  and  the  probable 
laws  of  their  arrangement.  If  the  stars  were  all  of  the  same 
intrinsic  brightness,  we  could  make  a  very  good  estimate  of 
their  distance  from  their  apparent  magnitude ;  but  we  know 
that  such  is  not  the  case.  Still,  in  all  reasonable  probability, 
the  diversity  of  absolute  magnitude  is  far  less  than  that  of  the 
apparent  magnitude;  so  that  a  judgment  founded  on  the  lat- 
ter is  much  better  than  none  at  all.  It  was  on  such  consider- 
ations as  these  that  the  conjectures  of  the  first  observers  with 
the  telescope  were  founded. 

§  1 .  Views  of  Astronomers  hefore  Herschel. 

Before  the  invention  of  the  telescope,  any  well-founded 
opinion  respecting  the  structure  of  the  starry  system  was  out 
of  the  question.  We  have  seen  how  strong  a  hold  the  idea  of 
a  spherical  universe  had  on  the  minds  of  men,  so  that  even 
Copernicus  was  fully  possessed  with  it,  and  probably  believed 
the  sun  to  be,  in  some  way,  the  centre  of  this  sphere.  Before 
any  step  could  be  taken  towards  forming  a  true  conception  of 
the  universe,  this  idea  had  to  be  banished  from  the  mind,  and 
the  sun  had  to  be  recognized  as  simply  one  of  innumerable 
stars  which  made  up  the  universe.  The  possibility  that  such 
might  have  been  the  case  seems  to  have  first  suggested  itself 
to  Kepler,  though  he  was  deterred  from  completely  accepting 
the  idea  by  an  incorrect  estimate  of  the  relative  brilliancy  of 
the  stars.  He  reasoned  that  if  the  sun  were  one  of  a  vast 
number  of  fixed  stars  of  equal  brilliancy  scattered  uniformly 
throughout  space,  there  could  not  be  more  than  twelve  which 
were  at  the  shortest  distance  from  us.  We  should  then  have 
another  set  at  double  the  distance,  another  at  triple  the  dis- 
tance, and  so  on ;  and  since  the  more  distant  they  are,  the 
fainter  they  would  appear,  we  should  speedily  reach  a  limit 
beyond  which  no  stars  could  be  seen.  In  fact,  however,  we 
often  see  numerous  stars  of  the  same  magnitude  crowded 
closely  together,  as  in  the  belt  of  Orion,  while  the  total  num- 
ber of  visible  stars  is  reckoned  by  thousands.     He  therefore 


474  THE  STELLAR   UNIVERSE. 

concludes  that  the  distances  of  the  individual  stars  from  each 
other  are  much  less  than  their  distances  from  our  sun,  the  lat- 
ter being  situated  near  the  centre  of  a  comparatively  vacant 
region. 

Ilad  Kepler  known  that  it  would  require  the  light  of  a  hun- 
dred stars  of  the  sixth  magnitude  to  make  that  of  one  of  the 
first  magnitude,  he  would  not  have  reached  this  conclusion. 
A  simple  calculation  would  have  shown  him  that,  with  twelve 
stars  at  distance  unity,  there  would  have  been  four  times  that 
number  at  the  double  distance,  nine  times  at  the  treble  dis- 
tance, and  so  on,  until,  within  the  tenth  sphere,  there  would 
have  been  more  than  four  thousand  stars.  The  twelve  hun- 
dred stars  on  the  surface  of  the  tenth  sphere  would  have 
been,  by  calculation,  of  the  sixth  magnitude,  a  number  near 
enough  to  that  given  by  actual  count  to  show  him  that  the 
hypothesis  of  a  uniform  distribution  was  quite  accordant  with 
observations.  It  is  true  that,  where  many  bright  stars  were 
found  crowded  together,  as  in  Orion,  their  distance  from  each 
other  is  probably  less  than  that  from  our  sun.  But  this  ag- 
glomeration, being  quite  exceptional,  would  not  indicate  a  gen- 
eral crowding  together  of  all  the  stars,  as  Kepler  seemed  to 
suppose.  In  justice  to  Kepler  it  must  be  said  that  he  put 
forth  this  view,  not  as  a  well-founded  theory,  but  only  as  a 
surmise,  concerning  a  question  in  Avhicli  certainty  was  not 
attainable. 

Ideas  of  Kant. — Those  who  know  of  Kant  only  as  a  specula- 
tive philosopher  may  l)e  surprised  to  learn  that,  although  he 
was  not  a  workiug  astronomer,  he  was  the  author  of  a  theory 
of  the  stellar  system  which,  with  some  modifications,  has  been 
very  generally  held  until  the  present  time.  Seeing  the  Gal- 
axy encircle  the  heavens,  and  knowing  it  to  be  produced  by 
the  light  of  innumerable  stars  too  distant  to  be  individually 
visible,  he  concluded  that  the  stellar  system  extended  much 
farther  in  the  direction  of  the  Galaxy  than  it  did  elsewhere. 
In  other  words,  he  conceived  the  stars  to  be  arranged  in  a 
comparatively  thin,  flat  layer,  or  stratum,  our  sun  being  some- 
where near  the  centre.     When  we  look  edgewise  along  this 


VIEWS  OF  MODERN  ASTRONOMERS.  475 

stratum,  we  see  an  immense  number  of  stars,  but  in  the  per- 
pendicular direction  comparatively  few  are  visible.* 

This  thin  stratum  suggested  to  Kant  the  idea  of  a  certain 
resemblance  to  the  solar  system.  Owing  to  the  small  inclina- 
tions of  the  planetary  orbits,  the  bodies  which  compose  this 
system  are  spread  out  in  a  thin  layer,  as  it  were ;  and  we  have 
only  to  add  a  great  multitude  of  planets  moving  around  the 
sun  in  orbits  of  varied  inclinations  to  have  a  representation  in 
miniature  of  the  stellar  system  as  Kant  imagined  it  to  exist. 
Had  the  zone  of  small  planets  between  Mars  and  Jupiter  then 
been  known,  it  would  have  afforded  a  striking  confirmation  of 
Kant's  view  by  showing  a  yet  greater  resemblance  of  the  plan- 
etary system  to  his  supposed  stellar  system.  Were  the  num- 
ber of  these  small  planets  sufficiently  increased,  we  should  see 
them  as  a  sort  of  Galaxy  around  the  zodiac,  a  second  Milky 
Way,  belonging  to  our  system,  and  resolvable  with  the  tele- 
scope into  small  planets,  just  as  the  Galaxy  is  resolved  into 
small  stars.  The  conclusion  that  two  systems  which  were  so 
similar  in  appearance  were  really  alike  in  structui'e  would 
have  seemed  very  well  founded  in  analogy. 

As  the  planets  are  kept  at  their  proper  distances,  and  pre- 
vented  from  falling  into  each  other  or  into  the  sun  by  the 
centrifugal  force  generated  by  their  revolutions  in  their  or- 
bits, so  Kant  supposed  the  stars  to  be  kept  apart  by  a  revolu- 
tion around  some  common  centre.  The  proper  motions  of 
the  stars  were  then  almost  unknown,  and  the  objection  was 
anticipated  that  the  stars  were  found  to  occupy  the  same  po- 
sition in  the  heavens  from  generation  to  generation,  and  there- 
fore could  not  be  in  motion  around  a  centre.  To  this  Kant's 
reply  was  that  the  time  of  revolution  was  so  long,  and  the 
motion  so  slow,  that  it  was  not  perceptible  with  the  imper- 
fect means  of  observation  then  available.  Future  genera- 
tions would,  he  doubted  not,  by  comparing  their  observations 


*  The  original  idea  of  this  theory  is  attributed  by  Kant  to  Wright,  of  Durham, 
England,  a  writer  whose  works  are  entirely  unknown  in  this  country,  and  whos( 
authorship  of  the  theory  has  been  very  generally  forgotten. 


476  THE  STELLAB  UNIVERSE. 

with  those  of  their  predecessors,  find  that  there  actually  was  a 
motion  among  the  stars. 

This  conjecture  of  Kant,  that  the  stars  would  be  found  to 
have  a  proper  motion,  has,  as  we  have  seen,  been  amply  con- 
firmed ;  but  the  motion  is  not  of  the  kind  which  his  theory 
would  require.  On  this  theory,  all  the  stars  ought  to  move  ia 
directions  nearly  parallel  to  tliat  of  the  Milky  Way,  just  as  in 
the  planetary  system  we  find  them  all  moving  in  directions 
nearly  parallel  to  the  ecliptic.  But  the  proper  motions  actually 
observed  have  no  common  direction,  and  follow  no  law  what- 
ever, except  that,  on  the  average,  there  is  a  preponderance  of 
motions  from  tlie  constellation  Hercules,  which  is  attributed 
to  an  actual  motion  of  our  sun  in  that  direction.  Making  al- 
lowance for  this  preponderance,  we  find  the  stars  to  be  appar- 
ently moving  at  random  in  every  direction ;  and  therefore 
they  cannot  be  moving  in  any  regularly  arranged  orbits,  as 
Kant  supposed.  A  defender  of  Kant's  system  might  indeed 
maintain  that,  as  it  is  only  in  a  few  of  the  stars  nearest  us 
that  any  proper  motion  has  been  detected,  the  great  cloud  of 
stars  which  make  up  the  Milky  Way  might  reall}'  be  moving 
along  in  regular  order,  a  view  the  possibility  of  which  we  shall 
be  better  prepared  to  consider  hereafter. 

The  Kantian  theory  supposes  the  system  which  we  have 
just  been  describing  to  be  formed  of  the  immense  stratum  of 
stars  which  make  up  the  Galaxy  and  stud  our  heavens,  and 
to  include  all  the  stars  separately  visible  with  our  telescopes. 
But  he  did  not  suppose  this  system,  immense  though  it  is,  to 
constitute  the  whole  material  universe.  In  the  nebulse  he 
saw  other  similar  systems  at  distances  so  immense  that  the 
combined  light  of  their  millions  of  suns  only  appeared  as  a 
faint  cloud  in  the  most  powerful  telescopes.  This  idea  that 
the  nebulee  were  other  galaxies  was  more  or  less  in  vogue 
among  popular  writers  until  a  quite  recent  period,  when  it 
was  refuted  by  the  spectroscope,  which  shows  that  these  ob- 
jects are  for  the  most  part  masses  of  glowing  gas.  It  has, 
however,  not  received  support  among  astronomers  since  thii 
time  of  Sir  AVilliam  HerscheL 


RESEARCHES  OF  HERSCHEL  AND  HIS  SUCCESSORS.     477 

System  of  Lambert. — A  few  years  after  the  appearance  of 
Kant's  work,  a  similar  but  more  elaborate  system  was  sketched 
out  by  Lambert.  He  supposed  the  universe  to  be  arranged  in 
systems  of  different  orders.  The  smallest  systems  which  we 
know  are  those  made  up  of  a  planet,  with  its  satellites  circu- 
lating around  it  as  a  centre.  The  next  system  in  order  of 
magnitude  is  a  solar  system,  in  which  a  number  of  smaller 
systems  are  each  carried  round  the  sun.  Each  individual  star 
which  we  see  is  a  sun,  and  has  its  retinue  of  planets  revolving 
around  it,  so  that  there  are  as  many  solar  systems  as  stars. 
These  systems  are  not,  however,  scattered  at  random,  but  are 
divided  up  into  greater  systems  which  appear  in  our  telescopes 
as  clusters  of  stars.  An  immense  number  of  these  clustei*s 
make  up  our  Galaxy,  and  form  the  visible  universe  as  seen  in 
our  telescopes.  There  may  be  yet  greater  systems,  each  made 
up  of  galaxies,  and  so  on  indefinitely,  only  their  distance  is  so 
immense  as  to  elude  our  observation. 

Each  of  the  smaller  systems  visible  to  us  has  its  central  body, 
the  mass  of  which  is  much  greater  than  that  of  those  which 
revolve  around  it.  This  feature  Lambert  supposed  to  extend 
to  other  systems.  As  the  planets  are  larger  than  their  satel- 
lites, and  the  sun  larger  than  its  planets,  so  he  supposed  each 
stellar  cluster  to  have  a  great  central  body  around  which  each 
solar  system  revolved.  As  these  central  bodies  are  invisible  to 
us,  he  supposed  them  to  be  opaque  and  dark.  All  the  systems, 
from  the  smallest  to  the  greatest,  were  supposed  to  be  bound 
together  by  the  one  universal  law  of  gravitation. 

As  not  the  slightest  evidence  favoring  the  existence  of  these 
opaque  centres  has  ever  been  found,  we  are  bound  to  say  that 
this  sublime  idea  of  Lambert's  has  no  scientific  foundation. 
Astronomers  have  handed  it  o\er  without  reservation  to  the 
lecturers  and  essayists. 

§  2.  Researches  of  Herschel  and  his  Successors. 

Herschel  was  the  first  who  investigated  the  structure  of 
the  stellar  system  by  a  long-continued  series  of  observations, 
executed  with  a  definite  end  in  view.     His  plan  was  that  of 


47S  THE  STELLAR   UNIVERSE. 

"  Star  -  gauging,"  which  meant,  in  the  first  place,  the  simple 
enumeration  of  all  the  stai-s  visible  M'ith  a  powerful  tele- 
scope in  a  given  portion  of  the  heavens.  He  emplo3-ed  a 
telescope  of  twenty  inches  aperture,  magnifying  one  hundred 
and  sixty  times,  the  field  of  view  being  a  quarter  of  a  degree 
in  diameter.  This  diameter  was  about  half  that  of  the  full 
moon,  so  that  each  count  or  gauge  included  all  the  stars  visi- 
ble in  a  space  having  one-fourth  the  apparent  surface  of  the 
lunar  disk.  From  the  number  of  stars  in  any  one  field  of 
view,  he  concluded  to  what  relative  distance  his  sight  ex- 
tended, supposing  a  uniform  distribution  of  the  stars  through- 
out all  the  space  included  in  the  cone  of  sight  of  the  telescope. 
When  an  observer  looks  into  a  telescope  pointed  at  the  heav- 
ens, his  field  of  vision  includes  a  space  which  constantly 
widens  out  on  all  sides  as  the  distance  becomes  greater ;  and 
the  reader  acquainted  with  geometry  will  see  that  this  space 
forms  a  cone  having  its  point  in  the  focus  of  the  telescope,  and 
its  circular  base  at  the  extreme  distance  to  which  the  telescope 
reaches.  The  solid  contents  of  this  cone  will  be  proportional 
to  the  cube  of  the  distance  to  which  it  extends ;  for  instance, 
if  the  telescope  penetrates  twice  as  far,  the  cone  of  sight  will 
be  not  only  twice  as  long,  but  the  base  will  be  twice  as  wide 
in  each  direction,  so  that  the  cone  will  have  altogether  eight 
times  the  contents,  and  will,  on  Herschel's  hypothesis,  contain 
eisrht  times  as  many  stars.  So,  when  Herschel  found  the  stars 
eight  times  as  numerous  in  one  region  as  in  another,  he  con- 
cluded that  the  stellar  system  extended  twice  as  far  in  the 
direction  of  the  first  region. 

To  count  all  the  stars  visible  with  his  telescope,  Herschel 
found  to  be  out  of  the  question.  He  would  have  had  to  point 
his  instrument  several  hundred  thousand  times,  and  count  all 
the  visible  stars  at  each  pointing.  He  therefore  extended  his 
survey  only  over  a  wide  belt  extending  more  than  half-way 
round  the  celestial  sphere,  and  cutting  the  Galaxy  at  right 
angles.  In  this  belt  he  counted  the  stars  in  3400  telescopic 
fields.  Comparing  the  average  number  of  stars  in  different 
regions  with  the  position  of  the  region  relative  to  the  Galaxy, 


RESEARCHES   OF  HERSCHEL  AND  HIS  SUCCESSORS.     479 

he  found  that  the  stars  were  thinnest  at  the  point  most  distant 
from  the  Galaxy,  and  that  they  constantly  increased  in  num- 
ber as  the  Galaxy  was  approached.  The  following  table  will 
give  an  idea  of  the  rate  of  increase.  It  shows  the  avei-age 
number  of  stars  in  the  field  of  view  of  the  telescope  for  each 
of  six  zones  of  distance  from  the  Galaxy. 

First  zone 90°  to  75°  from  Galaxy 4  stars  per  field. 

yeeoiul  zone 75°  "  G0°     "         "     ' 5       "         " 

Third  zone G0°  "  45°     "         "       8       "         " 

Fourth  zone 45°  "  30^     "         "       14       "         " 

Fifth  zone 30°  "  15°     "         "       24       "         " 

Sixth  zone 15°"     0°     "         "       53       "         " 

A  similar  enumeration  was  made  by  Sir  John  Herschel  for  the 
corresponding  region  on  the  other,  or  southern,  side  of  the  Gal- 
axy. He  used  the  same  telescope,  and  the  same  magnifying 
power.     His  results  were : 


First  zone G  stars  per  field. 

Second  zone 7       "         " 

Third  zone 9       "         " 


Fourth  zone 13  stars  per  field. 

Fifth  zone L'G       "         " 

Sixth  zone 59       "         '* 


The  reader  will,  perhaps,  more  readily  grasp  the  significa- 
tion of  these  nnmbei-s  by  the  mode  of  representation  which 
was  suggested  in  describing  the  distribution  of  the  nebulae. 
Let  him  imagine  himself  standing  under  a  clear  sk}'  at  the 
time  when  the  Milky  Way  encircles  the  horizon.  Tlien,  the 
first  zone,  as  we  have  defined  it,  will  be  around  the  zenith,  ex- 
tending one -sixth  of  the  way  to  the  horizon  on  every  side; 
the  second  zone  will  be  next  below  and  around  this  circular 
space,  extending  one-third  of  the  way  to  the  horizon ;  and  so 
each  one  will  follow  in  regular  order  until  we  reach  the  sixth, 
or  galactic,  zone,  which  will  encircle  the  horizon  to  a  height 
of  15°  on  every  side.  The  numbers  we  have  given  show  that 
in  the  position  of  the  observer  which  we  have  supposed  the 
stars  would  be  thinnest  around  the  zenith,  and  would  con- 
stantly increase  in  number  as  we  approached  the  horizon. 
The  observer  being  supposed  still  to  occupy  the  same  posi- 
tion, the  second  table  shows  the  distribution  of  the  stars  in  ths 

32 


480  THE  STELLAR   UNIVERSE. 

opposite  or  invisible  hemisphere,  which  he  would  see  if  the 
earth  were  removed.  In  this  hemisphere  the  first,  or  thinnest, 
zone  would  be  directly  opposite  tlie  thinnest  zone  in  the  ob- 
server's zenith  ;  that  is,  it  would  be  directly  nnder  his  feet. 
The  successive  zones  would  then  be  nearer  the  horizon,  the 
sixth  or  last  encircliug  it,  and  extending  15°  below  it  on  evei7 
side. 

The  numbers  we  have  given  are  only  averages,  and  do  not 
give  an  adequate  idea  of  the  actual  inequalities  of  distribu- 
tion in  special  regions  of  the  heavens.  Sometimes  there  was 
not  a  solitary  star  in  the  field  of  the  telescope,  while  at  oth- 
ers there  were  many  hundreds.  In  the  circle  of  the  Galaxy 
itself,  the  stars  are  more  than  twice  as  thick  as  in  the  average 
of  the  first  zone,  which  includes  not  only  this  circle,  but  a 
space  of  15°  on  each  side  of  it. 

Adopting  the  hypothesis  of  a  uniform  distribution  of  tho 
stars,  Hei-schel  concluded  from  his  first  researclies  tliat  the 
stellar  system  was  of  the  general  form  supposed  l)y  Kant,  ex- 
tending out  on  all  sides  five  times  as  far  in  the  direction  of 
the  Galaxy  as  in  the  direction  perpendicular  to  it.  The  most 
important  modification  he  made  was  to  suppose  an  immense 
cleft  extending  edgewise  into  the  system  from  its  circumfer- 
ence about  half-way  to  the  centre.  This  cleft  corresponded  to 
the  division  in  the  Milky  Way  which  commences  in  the  sum- 
mer constellation  Cygnus  in  the  north,  and  passes  through 
Aquila,  the  Serpent,  and  Scorpius  far  into  the  southern  hemi- 
sphere. Estimating  tlie  distance  by  the  arrangement  and  ap- 
parent magnitude  of  the  stars,  lie  was  led  to  estimate  the  mean 
thickness  of  the  stellar  stratum  fi-om  top  to  bottom  as  155 
units,  and  the  diameter  as  850  units,  the  unit  being  the  aver- 
age distance  of  a  star  of  the  first  magnitude.  Supposing  this 
distance  to  be  that  which  light  would  travel  over  in  16  yeare 
— a  supposition  which  is  founded  on  the  received  estimate  of 
the  mean  parallax  corres])ouding  to  stars  of  that  magnitude — 
then  it  would  take  light  nearly  14,000  years  to  ti-avol  across 
the  system  from  one  border  to  the  other,  and  7000  years  to 
reach  us  from  the  extreme  boundarv. 


RESEARCHES  OF  RERSCHEL  AXD  HIS  SUCCESSORS.     481 


Tlie  foregoing  deduction  of 
Herscliel  was  founded  on  the 
hypothesis  that  the  stars  ^vere 
equally  dense  in  every  part  of 
the  stellar  system,  so  that  the 
number  of  stars  in  any  direc- 
tion furnished  an  index  to  the 
extent  of  the  stars  in  that  di- 
rection. Further  study  show- 
ed Herschel  that  this  assump- 
tion might  be  so  far  from  cor- 
rect that  his  conclusions  would 
have  to  be  essentially  modi- 
tied.  Binary  and  other  double 
stars  and  star  clusters  evident- 
ly offered  cases  in  which  sev- 
eral stai-s  were  in  much  closer 
association  than  were  the  stars 
in  general.  To  show  exactly 
on  what  considerations  this 
change  of  view  is  founded,  we 
remark  that  if  the  increase  of 
density'  in  the  direction  of  the 
Milky  Way  were  quite  regu- 
lar, so  that  there  were  no  cases 
of  great  difference  in  the  thick- 
ness of  the  stars  in  two  adjoin- 
ing regions,  then  the  original 
■view  would  have  been  sound 
so  far  as  it  went.  But  such  ir- 
a-egularities  are  very  frequent, 
and  it  would  lead  to  an  obvi- 
ous absurdity  to  explain  them 
on  Ilerschel's  first  hypothesis  ; 
for  instance,  when  the  tele- 
scope was  du-ected  towards 
*he  Pleiades  there  would  be 


FiQ.  10'.).— Hei'schel's  view  of  the  form  of  thg 
univeree. 


482  THE  STELLAR   UNIVERSE. 

found,  probably,  six  or  eight  times  as  many  stare  as  in  the  ad- 
joining fields.  But  supposing  the  real  thickness  of  the  stars 
the  same,  the  result  would  be  that  in  this  particular  direction 
the  stars  extended  out  twice  as  far  as  they  did  in  the  neigh- 
boring parts  of  the  sky ;  that  is,  we  should  have  a  long,  nar- 
row spike  of  stars  pointing  directly  from  us.  As  there  are 
many  such  clusters  in  vario^is  parts  of  the  sky,  we  should  have 
to  suppose  a  great  number  of  such  spikes.  In  other  regions, 
especially  around  the  Milky  Way,  there  are  spaces  nearly  void 
of  stars.  To  account  for  these  we  should  have  to  suppose 
long  narrow  chasms  reaching  through  towards  our  sun.  Thus 
the  stellar  system  would  present  the  form  of  an  exaggerated 
etar-fish  with  numerous  deep  openings,  a  form  the  existence 
of  which  is  beyond  all  probability,  especially  if  we  reflect 
that  all  the  openings  and  all  the  arms  have  to  proceed  from 
the  direction  of  our  sun. 

The  only  rational  explanation  of  a  group  of  stars  showing 
itself  in  a  telescope,  with  a  comparatively  void  space  surround- 
ing it,  is  that  we  have  here  a  real  star  clustei-,  or  a  region  in 
which  the  stars  are  thicker  than  elsewhere.  Xow,  one  can  see 
with  the  naked  eye  that  the  Milky  Way  is  not  a  continuous 
uniform  belt,  but  is,  thi-ough  much  of  its  course,  partly  made 
up  of  a  great  number  of  irregular  cloud-like  masses  with  com- 
paratively dark  spaces  between  them.  The  conclusion  is  un- 
avoidable tliat  we  have  here  real  aggregations  of  stars,  and 
not  merely  a  region  in  which  the  bounds  of  the  stellar-sys- 
tem are  more  widely  extended.  Whether  Ilerschel  clearly  saw 
this  may  be  seriously  questioned ;  but  however  it  may  have 
been,  he  adopted  another  method  of  estimating  the  relative 
distances  of  the  stars  visible  in  his  gauges. 

This  method  consisted  in  judging  of  the  distances  to  which 
his  telescope  penetrated,  not  by  the  number  of  stars  it  brought 
into  view,  but  by  their  brightness.  If  all  the  stars  were  of  the 
same  intrinsic  brightness,  so  that  the  differences  of  their  ap- 
parent magnitude  arose  only  from  their  various  distances  from 
us,  then  this  method  would  enable  us  to  fix  the  distance  of 
each  separate  star.     But  as  we  know  that  the  stars  are  by  no 


EESE ARCHES  OF  EEBSCHEL  AND  HIS  SUCCESSORS.     483 


means  equal  in  intrinsic  brightness,  the  method  cannot  be 
safely  applied  to  any  individual  star,  a  fact  which  Ilerschel 
himself  clearly  saw.  It  does  not  follow,  however,  that  we 
cannot  thus  form  an  idea  of  the  relative  distances  of  whole 
classes  or  groups  of  stars.  Although  it  is  quite  possible  that 
an  individual  star  of  the  fifth  magnitude  may  be  nearer  to  us 
than  another  of  the  fourth,  yet  we  cannot  doubt  that  the  av- 
erage distance  of  all  the  fifth-magnitude  stars  is  greater  than 
the  average  of  those  of  the  fourth  magnitude,  and  greater, 
too,  in  a  proportion  admitting  of  a  tolerably  accurate  numeri- 
cal estimate.  Such  an  estimate  Ilerschel  attempted  to  make, 
proceeding  on  the  following  plan : 

Suppose  a  sphere  to  be  drawn  around  our  sun  as  a  centre 
of  such  size  that  it  shall  be 
equal  to  the  average  space 
occupied  by  a  single  one  of 
the  stars  visible  to  the  naked 
eye;  that  is,  if  we  suppose 
that  portion  of  the  space  of 
the  stellar  system  occupied 
by  the  six  thousand  bright- 
er stars  to  be  divided  into 
six  thousand  parts,  then  the 
sphere  will  be  equal  to  one 
of  these  parts.  The  radius 
of  this  sphere  will  probably 
not  differ  much  from  the  dis- 
tance of  the  nearest  fixed  star, 
a  distance  we  shall  take  for 
unity.  Then,  suppose  a  series 
of  larger  spheres,  all  drawn 
around  our  sun  as  a  centre, 
and  having  the  radii  3,  5,  7, 
9,  etc.  The  contents  of  the 
spheres  being  as  the  cubes 
of  their  diameters,  the  first  ^.    ,,„    .,,    ,   ..     „     ,  „      ,       , .. 

'  Fig.  110.— Illustratiug  Herschel's  orders  of  dis- 

ephere  will  have  3x3x3=27  tance  of  the  stars. 


484 


THE  STELLAE   VyiVERSE. 


times  the  bulk  of  the  unit  sphere,  and  will  therefore  be  large 
enoiicrh  to  contain  27  stars;  the  second  will  have  125  times 
the  bulk,  and  will  therefore  contain  125  stai-s,  and  so  with 
the  successive  spheres.  Fig.  110  shows  a  section  of  portions 
of  these  spheres  up  to  that  with  radius  11.  Above  the  centre 
are  given  the  various  ordei-s  of  stars  which  are  situated  be° 
twceu  the  several  spheres,  while  in  the  corresponding  spaces 
below  the  centre  are  given  the  number  of  stare  which  the  re- 
gion is  large  enough  to  contain ;  for  instance,  the  sphere  of 
radius  7  has  room  for  343  stai-s,  but  of  this  space  125  parts 
belong  to  the  spheres  inside  of  it :  there  is,  tlierefore,  room  for 
21S  stars  between  the  spheres  of  radii  5  and  7. 

Herschel  designates  the  several  distances  of  these  layers  of 
stare  as  orders ;  the  stare  between  spheres  1  and  3  are  of  the 
firet  order  of  distance,  those  between  3  and  5  of  the  second 
order,  and  so  on.  Comparing  the  room  for  stars  between  the 
several  spheres  with  the  number  of  stare  of  the  several  magni- 
tudes, he  found  the  result  to  be  as  follows : 


Order  of 
DisUnc«. 

Number  of 

Number  of 

Stars  ther« 

Magnitade. 

Stars  of  that 

U  room  for. 

ma^itade. 

1 

26 

1 

17 

2 

98 

2 

r.7 

3 

218 

3 

206 

4 

386 

4 

454 

5 

602 

o 

1161 

6 

866 

G 

6103 

7 

1178 

7 

6146 

8 

1538 

There  is  evidently  no  correspondence  between  the  calculat- 
ed ordere  of  distance  and  the  magnitudes  as  estimated  on  the 
usual  scale.  But  Herechel  found  that  this  was  because  the 
magnitudes  as  usually  estimated  corresponded  to  an  entirely 
different  scale  of  distance  from  that  which  he  adopted.  In 
his  scale  the  several  distances  increased  in  arithmetical  pro- 
gression ;  while  in  the  order  of  magnitudes  the  increase  is 
in  geometrical  progression.  In  consequence,  tlie  stars  of  the 
sixth  magnitude  correspond  to  the  eighth,  ninth,  or  tenth  order 
of  distances ;  that  is,  we  should  have  to  remove  a  star  of  the 


BESE ARCHES  OF  HEBSCHEL  AND  HIS  SUCCESSOBS.     4^5 

first  magnitude  to  eight,  nine,  or  ten  times  its  actual  distance 
to  make  it  shine  as  a  star  of  the  sixth  magnitude. 

Attempting  on  this  system  to  measure  the  extent  of  tlie 
Milky  Way,  Herschel  concluded  that  it  was  unfathomable 
witli  his  twenty -foot  telescope,  which,  he  calculated,  would 
penetrate  to  the  900th  order  of  distances,  that  is,  to  stars 
which  were  900  times  as  far  as  the  average  of  those  of  the 
first  magnitude.  lie  does  not  seem  to  have  made  any  very 
extended  examination  with  his  forty-foot  telescope,  but  con- 
chided  that  it  would  leave  him  in  the  sauie  uncertainty  in 
respect  to  the  extent  of  the  Milky  Way  as  the  twenty-foot  one 
did.  This  unrivalled  man,  to  whom  it  was  given  to  penetrate 
farther  into  creation  than  man  had  ever  done  before  him, 
seems  to  have  rested  from  his  labors  without  leaving  any  more 
definite  theory  of  the  boundaries  of  the  stellar  system  than 
that  they  extended,  at  least  in  the  direction  of  the  Milky  Way, 
beyond  the  utmost  limit  to  which  his  telescope  could  penetrate. 
If  we  estimate  the  tin)e  it  would  require  light  to  come  from 
the  utmost  limit  to  which  he  believed  his  vision  to  extend, 
we  shall  find  it  to  be  about  fourteen  thousand  years,  or  more 
than  double  that  deduced  from  liis  former  gauges.  We  can 
say  with  confidence  that  the  time  required  for  light  to  reach 
us  from  the  most  distant  visible  stars  is  measured  by  thou- 
sands of  years.  But  it  must  be  admitted  that  Ilerschel's  esti- 
mate of  the  extent  of  the  Milky  Way  may  be  far  too  great,  be- 
cause it  rests  on  the  assumption  that  all  stars  are  of  the  same 
absolute  brightness.  If  the  smallest  stars  visible  in  his  tele- 
scope were,  on  the  average,  of  the  same  intrinsic  brilliancy  as 
the  brighter  ones,  the  conclusion  would  be  well  founded.  But 
if  we  suppose  a  boundary,  it  is  impossible  to  decide  from  Her- 
Bchel's  data  whether  the  minuteness  of  those  stars  arises  from 
their  great  distance  or  from  their  small  magnitude.  Notwith- 
standing this  uncertainty,  it  has  lieen  maintained  by  some,  not- 
ably by  Mr.  Proctor,  that  the  views  of  Herschel  respecting  the 
constitution  of  the  Milky  Way,  or  stellar  system,  were  radical 
ly  changed  by  this  second  method  of  star-gauging.  I  see  no 
evidence  of  any  radical  change.     Although  Herschel  does  not 


486  THE  STELLAR   UNIVERSE. 

express  himself  very  definitely  on  the  .subject,  yet,  in  his  last 
paper  on  the  distribution  of  the  stars  {Philosophical  Trans- 
actions for  1S17),  there  are  several  remarks  which  seem  to  im- 
ply that  ]ie  still  supposed  the  stellar  system  to  have  the  gen- 
eral form  shown  in  Fig.  109,  and  tliat,  in  accordance  with  tliat 
view,  he  supposed  the  clustering  of  stars  to  indicate  protuber- 
ant parts  of  the  Milky  Way.  He  did,  indeed,  apply  a  differ- 
ent method  of  research,  but  the  results  to  which  the  new  meth- 
ods led  were,  in  their  main  features,  the  same  as  those  of  the 
old  method. 

Since  the  time  of  Herschel,  one  of  the  most  eminent  of  the 
astronomers  who  have  investigated  this  subject  is  Strnve  the 
elder,  formerly  director  of  tlie  Pulkowa  Observatory.  His  re- 
searclies  were  founded  mainly  on  the  numbers  of  stars  of  the 
several  magnitudes  found  by  Bessel  in  a  zone  thirty  degrees 
wide  extending  all  round  the  heavens,  fifteen  degrees  on  each 
side  of  the  equator.  With  these  lie  combined  the  gauges  of 
Sir  William  Hei-schel.  The  hypothesis  on  which  he  based  his 
theory  was  similar  to  that  employed  by  Herschel  in  his  later 
researches,  in  so  far  that  he  supposed  the  magnitude  of  the 
stai*s  to  furnish,  on  tlie  average,  a  measure  of  their  relative 
distances.  Supposing,  after  Herschel,  a  number  of  concentric 
spheres  to  be  drawn  around  the  sun  as  a  centre,  the  successive 
spaces  between  which  corresponded  to  stars  of  the  several 
magnitudes,  he  found  that  the  farther  out  he  went,  tlie  more 
the  stars  were  condensed  in  and  near  the  Milky  V^ay.  This 
conclusion  may  be  drawn  at  once  from  the  fact  we  have  al- 
ready mentioned,  that  the  smaller  the  stars,  the  more  they  are 
condensed  in  the  region  of  the  Galaxy.  Strnve  found  that  if 
we  take  only  the  stars  plainly  visible  to  the  naked  eye — that 
is,  those  down  to  the  fifth  magnitude — they  are  no  thicker  in 
the  Milky  Way  than  in  other  parts  of  the  heavens.  But  those 
of  the  sixth  magnitude  are  a  little  thicker  in  that  region,  those 
of  the  seventh  yet  thicker,  and  so  on,  the  inequality  of  distri- 
bution becoming  constantly  greater  as  the  telescopic  power  is 
increased. 

From  all  this,  Struve  concluded  that  the  stellar  system  migh/ 


BESE ARCHES  OF  HEESCHEL  AND  HIS  SUCCESSORS.     487 

be  considered  as  composed  of  layers  of  stars  of  various  densi- 
ties, all  parallel  to  the  plane  of  the  Milky  Way.  The  stars  are 
thickest  in  and  near  tlie  central  layer,  which  lie  conceives  to 
be  spread  out  as  a  wide,  thin  sheet  of  stars.  Our  sun  is  situ- 
ated near  the  middle  of  this  layer.  As  we  pass  out  of  this 
layer,  on  either  side  we  find  the  stars  constantly  growing  thin- 
ner and  thinner,  but  we  do  not  reach  any  distinct  boundary. 
As,  if  we  could  rise  in  the  atmosphere,  we  should  find  the  air 
constantly  growing  thinner,  but  at  so  gradual  a  i-ate  of  prog- 
ress that  we  could  hardly  say  where  it  terminated  ;  so,  on 
Struve's  view,  would  it  be  with  the  stellar  system,  if  we  could 
mount  up  in  a  direction  perpendicular  to  the  Milky  Way. 
Struve  o-ives  the  following  table  of  the  thickness  of  the  stars 
on  each  side  of  the  principal  plane,  the  unit  of  distance  being 
that  of  the  extreme  distance  to  which  Ilerschel's  telescope 
could  penetrate : 


Mean  Distance 

Distance  from  Principal  Plane. 

Density. 

between  Keij^h- 
boring  Stars. 

In  the  principal  plane..... 

1.0000 

1.000 

0.05  from  principal  plane 

0.48568 

1.272 

0.10          "              "          

0.;!3'.'88 

1.4.58 

0.20          "              "          

0.23895 

1.611 

0.30          "              "          

0.17980 

1.772 

0.40           "              "          

0.13021 

1.973 

0.50          "              "          

0.08646 

2.261 

0.60          "              "          

0.0.5510 

2.628 

0.70          "              "          

0.03079 

3.190 

0.80          "              "          

0.01414 

4.131 

0.866        "              "          

0.00532 

5. 729 

This  condensation  of  the  stars  near  the  central  plane,  and 
the  gradual  thinning-out  on  each  side  of  it,  are  only  designed 
to  be  the  expression  of  the  general  or  average  distribution 
of  those  bodies.  The  probability  is  that  even  in  the  central 
plane  the  stars  are  many  times  as  thick  in  some  regions  as  in 
others,  and  that  as  we  leave  the  plane,  the  thinning-out  would 
be  found  to  proceed  at  very  different  rates  in  different  re- 
gions. That  there  may  be  a  gradual  thinning -out  cannot  be 
denied ;  but  Struve's  attempt  to  form  a  table  of  it  is  open  to 
the  serious  objection  that,  like  Ilerschel,  he  supposed  the  dli 
Y 


4,88  THE  STELLAR    UNIVEESE. 

fereiices  between  the  luagintiides  of  tlie  stars  to  arise  entirely 
from  their  different  distances  from  us.  Although  where  tlie 
scattering  of  the  stars  is  nearly  uniform  this  supposition  may 
not  lead  us  into  serious  error,  the  case  will  be  entirely  differ- 
ent where  we  have  to  deal  with  irregular  masses  of  stars,  and 
especially  where  our  telescopes  penetrate  to  the  boundary  of 
the  stellar  system.  In  the  latter  case  we  cannot  possibly  dis- 
tinguisli  between  small  stars  lying  within  the  boundary  and 
larger  ones  scattered  outside  of  it,  and  Struve's  gradual  thin- 
ning-out of  the  stars  may  be  entii'ely  accounted  for  by  great 
diversities  in  the  absolute  brightness  of  the  stars. 

Among  recent  researches  on  this  subject,  those  of  Mr.  R. 
A.  Proctor  are  entitled  to  consideration,  from  being  founded 
on  facts  which  were  not  fully  known  or  understood  by  the 
investigators  whom  we  have  mentioned.  The  strongest  point 
which  he  makes  is  that  all  views  of  the  arrangement  of  the 
stellar  system  founded  upon  the  theory  that  the  stars  are 
either  of  similar  intrinsic  brightness,  or  approach  an  equality 
of  distribution  in  different  regions,  are  entirely  illusory.  He 
cites  the  phenomena  of  star-drift,  described  in  the  last  chap- 
tei",  as  proving  that  stars  which  had  been  supposed  widely  se|> 
arated  are  reall}'  agglomerated  into  systems;  and  claims  that 
the  Milky  Way  may  be  a  collection  of  such  systems,  having 
nothing  like  the  extent  assigned  it  by  Ilerschel. 

How  far  the  considerations  brought  forward  by  Mr.  Proc- 
tor should  make  us  modify  the  views  of  the  subject  hitherto 
held,  cannot  be  determined  without  further  observations  on  the 
clustering  of  stars  of  different  magnitudes.  We  may,  howev- 
er, safely  concede  that  there  is  a  greater  tendency  among  the 
stars  to  be  collected  into  groups  than  was  formerly  supposed. 
A  curious  result  of  Mr.  J.  M.  Wilson,  of  Rugby,  England,  re- 
specting the  orbits  of  some  binary  stars,  throws  light  on  this 
tendency.  It  was  found  by  Struve  that  although  the  great 
common  proper  motion  of  the  pair  of  stars  61  Cygni,  cele- 
brated for  the  determinations  of  tlieir  parallax,  was  such  as  to 
leave  no  reasonable  doubt  that  they  were  physically  connect- 
ed, yet  not  the  slightest  deviation  in  their  courses,  arising 


RESEARCHES  OF  HEBSCHEL  AND  HIS  SUCCESSORS.     489 

from  their  mutual  attraction,  could  be  detected.  Mr.  Wilson 
has  recently  confirmed  this  result  by  an  examination  of  the 
whole  series  of  measures  on  this  pair  from  1753  to  1874, 
which  do  not  show  the  slightest  deviation,  but  seem  to  indi- 
cate that  each  star  of  the  pair  is  going  on  its  course  indepen- 
dently of  the  other.  But,  as  just  stated,  they  move  too  nearly 
together  to  permit  of  the  belief  that  they  are  really  indepen- 
dent. The  only  conclusion  open  to  us  is  that  each  of  them  de- 
scribes an  immense  orbit  around  their  connnon  centre  of  grav- 
ity, an  orbit  which  may  be  several  degrees  in  apparent  diam- 
eter, and  in  which  the  time  of  revolution  is  counted  by  thou- 
sands of  years.  Two  thousand  years  hence  they  will  be  so 
far  apart  that  no  connection  between  them  would  be  sus- 
pected. 

It  is  a  question  whether  we  ha\e  not  another  instance  of 
the  same  kind  in  the  double  star  Castor,  or  a  Geminorum. 
Mr.  Wilson  finds  the  orbit  of  this  binary  to  be  apparently 
hyperbolic,  a  state  of  things  which  would  indicate  that  the 
two  stars  had  no  physical  connection  whatever,  but  that,  in 
pursuing  their  courses  through  space,  they  chanced  to  come 
so  close  together  that  they  were  brought  for  a  while  within 
each  other's  sphere  of  attraction.  If  this  be  the  case,  they 
will  gradually  separate  forever,  like  two  ships  meeting  on  the 
ocean  and  parting  again.  We  remark  that  the  course  of  each 
star  will  then  be  very  different  from  what  it  would  have 
been  if  they  had  not  met.  We  cannot,  however,  accept  the 
hyperbolic  orbit  of  Mr.  Wilson  as  an  established  fact,  because 
the  case  is  one  in  which  it  is  very  difficult  to  distinguish  be- 
tween a  large  and  elongated  elliptic  orbit  and  a  hyperbolic 
orbit.  The  common  proper  motion  of  the  two  objects  is  such 
as  to  lead  to  the  belief  that  they  constitute  a  pair,  the  compo° 
nents  of  which  separate  to  a  great  distance. 

Now,  these  discoveries  of  pairs  of  stars  moving  around  a 
common  centre  of  gravity,  in  orbits  of  immense  extent,  sug- 
gest the  probability  that  there  exist  in  the  heavens  great  num- 
bers of  pairs,  clusters,  and  systems  of  this  sort,  the  members 
of  which  are  so  widely  separated  that  they  have  never  been 


490  THE  STELLAR   UNIVERSE. 

suspected  to  belong  together,  and  the  widel^^  scattered  groups 
having  a  common  proper  motion  may  very  well  be  systems  of 
this  kind. 

§  3.  Probable  Arrangement  of  the  Visible  Universe. 

The  preceding  description  of  the  views  held  by  several  gen- 
erations of  profound  thinkers  and  observers  respecting  the 
arrangement  of  the  visible  universe  furnishes  an  example  of 
what  we  may  call  the  evolution  of  scientific  knowledge.  Of 
no  one  of  the  great  men  whom  we  have  mentioned  can  it  be 
said  that  his  views  were  absolutely  and  unqualifiedly  errone- 
ous, and  of  none  can  it  be  said  that  lie  reached  tlie  entire 
truth.  Their  attempts  to  solve  tlie  mystery  which  they  saw 
before  them  were  like  those  of  a  spectator  to  make  out  the  ex- 
act structure  of  a  great  building  which  he  sees  at  a  distance 
in  the  dim  twilight.  He  first  sees  that  the  building  is  really 
there,  and  sketches  out  what  he  believes  to  be  its  outlines.  As 
the  light  increases,  he  finds  that  his  first  outline  bears  but  a 
rude  resemblance  to  what  now  seems  to  be  the  real  form,  and 
he  corrects  it  accordingly.  In  his  first  attempts  to  fill  in  the 
columns,  pilasters,  windows,  and  doors,  he  mistakes  the  darker 
shades  between  the  columns  for  windows,  other  lighter  sliad- 
ows  for  doors,  and  the  pilasters  for  columns.  Notwithstand- 
ing such  mistakes,  his  representation  is  to  a  certain  extent  cor- 
rect, and  he  will  seldom  fall  into  egregious  error.  The  suc- 
cessive improvements  in  his  sketch,  from  the  first  rough  out- 
line to  the  finished  picture,  do  not  consist  in  eflfacing  at  each 
step  everything  he  has  done,  but  in  correcting  it,  and  filling  in 
the  details. 

The  progress  of  our  knowledge  of  nature  is  generally  of  this 
character.  But  in  the  case  now  before  us,  so  great  is  the  dis- 
tance, so  dim  the  light,  and  so  slender  our  ideas  of  the  princi- 
ples on  which  the  vast  fabric  is  constructed,  that  we  cannot 
pass  beyond  a  few  rough  outlines.  Still  there  are  a  few  feat- 
ures wliich  we  can  describe  with  a  near  approach  to  certainty, 
and  others  respecting  which,  though  our  knowledge  is  some- 
what vague,  we  can  reach  a  greater  or  less  degree  of  proba- 


PROBABLE  ARRANGEMENT  OF  THE  VISIBLE  UNIVERSE.  491 

bility.  "We  may  include  these  under  the  following  seven 
heads : 

1st.  Leaving  the  nebulae  out  of  consideration,  and  confining 
ourselves  to  the  stellar  system,  we  may  say,  with  moral  cer- 
tainty, that  the  great  mass  of  the  stars  which  compose  this 
system  are  spread  out  on  all  sides,  in  or  near  a  widely  extend- 
ed plane  passing  through  the  Milky  Way.  In  other  words, 
the  large  majority  of  the  stars  which  we  can  see  with  the  tele- 
scope are  contained  in  a  space  having  the  form  of  a  round,  flat 
disk,  the  diameter  of  which  is  eight  or  ten  times  its  thickness. 
This  was  clearly  seen  by  Kant,  and  has  been  confirmed  by 
Herschel  and  Struve.  In  fact,  it  forms  the  fundamental  base 
of  the  structures  reared  by  these  several  investigators.  When 
Kant  saw,  in  this  ari-angement,  a  resemblance  to  the  solar 
system,  in  which  the  planets  all  move  round  near  one  central 
plane,  he  was  correct,  so  far  as  he  went.  The  space,  then,  in 
which  we  find  most  of  the  stars  to  be  contained  is  bounded 
by  two  parallel  planes  forming  the  upper  and  lower  surfaces 
of  the  disk  we  have  described,  the  distance  apart  of  these 
planes  being  a  small  fraction  of  their  extent  —  probably  less 
than  an  eighth. 

2d.  Within  the  space  we  have  described  the  stars  are  not 
scattered  utiiformly,  but  are  for  the  most  part  collected  into 
irregular  clusters  or  masses,  with  comparatively  vacant  spaces 
between  them.  These  collections  have  generally  no  definite 
boundaries,  but  run  into  each  other  by  insensible  gradations. 
The  number  of  stars  in  each  collection  may  range  from  two 
to  many  thousands ;  and  largei"  masses  are  made  up  of  smaller 
ones  in  every  proportion,  much  as  the  heavy  clouds  on  a  sum- 
mer's day  are  piled  upon  each  other. 

3d.  Our  sun,  with  its  attendant  planets,  is  situated  near  the 
centre  of  the  space  we  have  described,  so  that  we  see  nearly 
the  same  number  of  stars  in  any  two  opposite  quarters  of  the 
heavens. 

4th.  The  six  or  seven  thousand  stars  around  us,  which  are 
easily  seen  by  the  naked  eye,  are  scattered  in  space  witli  a 
near  approach  to  uniformity,  the  only  exception  being  local 


492  THE  STELLAR   UNIVERSE. 

clusters,  the  component  stars  of  which  are  few  in  number  and 
pretty  widely  separated.  Such  are  the  Pleiades,  Coma  Bere- 
nices, and  perhaps  the  principal  stars  of  many  other  constella- 
tions, which  are  so  widely  separated  that  we  do  not  see  any 
connection  among  them. 

5th.  The  disk  which  we  have  described  does  not  represent 
the  form  of  the  stellar  system,  but  only  the  limits  within 
which  it  is  mostly  contained.  The  absence  of  any  definite 
boundary,  either  to  star  clusters  or  the  stellar  system,  and  the 
number  of  comparatively  vacant  regions  here  and  there  among 
the  clusters,  prevent  our  assigning  any  more  definite  form  to 
the  system  than  we  could  assign  to  a  cloud  of  dust.  The  thin 
and  widely  extended  space  in  which  the  stars  are  most  thickly 
clustered  may,  however,  be  called  the  galactic  region. 

6th.  On  each  side  of  the  galactic  region  the  stars  are  more 
evenly  and  thinly  scattered,  but  probably  do  not  extend  out  to 
a  distance  at  all  approaching  the  extent  of  the  galactic  region. 
If  they  do  extend  out  to  an  equal  distance,  they  are  very  few 
in  number.  It  is,  however,  impossible  to  set  any  definite  boun- 
daries, not  only  from  our  ignorance  of  the  exact  distance  of 
the  smallest  stars  we  can  see  in  the  telescope,  but  because  the 
density  of  the  stars  probably  diminishes  very  gradually  as  we 
go  out  towards  the  boundary. 

Tth.  On  each  side  of  the  galactic  and  stellar  region  we  have 
a  nebular  region,  in  which  we  find  few  or  no  stai*s,  but  vast 
numbers  of  nebulae.  Tlie  nebulae  diminish  greatly  in  num- 
ber as  we  approach  the  galactic  region,  only  a  very  few  being 
found  in  that  region. 

The  general  arrangement  of  the  stars  and  nebulae  which  we 
have  described  is  seen  in  Fig.  Ill,  which  shows  what  is  prob- 
ably the  general  aspect  of  a  section  of  the  visible  universe  per- 
pendicular to  the  Milky  Way.  In  the  central  part  of  tlie  fig- 
ure we  have  the  galactic  region,  in  which  the  stars  are  mostly 
aggregated  in  large  masses.  Of  the  arrangement  of  these 
masses  nothing  certain  is  known :  they  are,  therefore,  put  in 
nearly  at  random.  Indeed,  it  is  still  an  undecided  question 
whether  tlie  aggregations  of  stars  which  make  up  the  Milky 


PROBABLE  ARRANGEMENT  OF  THE  VISIBLE  UNIVERSE.  493 

Way  extend  all  the  way  across  the  diameter  of  the  galactic 
region,  or  whether  they  are  ai-raiiged  in  the  form  of  a  ring, 
with  our  sun  and  his  surrounding  stars  in  the  centre  of  it. 
In  the  latter  case,  the  masses  of  stars  near  the  centre  should 
be  less  strongly  marked.  This  central  region  being  that  in 
wliich  our  earth  is  situated,  this  uncertainty  respecting  the 
density  of  stars  in  that  i-egion  implies  an  uncertainty  whether 


Fio.  111. — Probable  nrrangemeut  of  the  st.ii-s  and  nebulae  visible  with  the  telescope,    In 
the  Galaxy  the  stars  are  not  evenly  scatteied,  but  are  agglomerated  into  clusters. 

the  stars  visible  with  the  naked  eye  are  part  of  one  of  the 
masses  which  make  up  the  Galaxy,  or  whether  we  are  in  a 
comparatively  thin  region.  Although  this  question  is  still 
unsolved,  it  is  one  which  admits  of  an  answer  by  telescopic 
research.  When  we  described  Sir  William  llerschers  ar- 
rangement of  the  stars  in  concentric  spheres,  we  saw  that  in 
the  more  distant  spheres  the  stars  were  vastly  more  dei'ee 


494  THE  STELLAS   UXIVEBSE. 

around  the  galactic  belt  of  each  sphere  than  they  were  in 
other  parts  of  it.  To  answer  the  question  which  has  been 
presented,  we  must  compare  the  densities  of  the  stars  at  the 
circumferences  of  these  spheres  with  the  density  immediately 
around  us.  In  other  words,  the  question  is,  Suppose  a  human 
being  could  dart  out  in  the  direction  of  the  Milky  "Way,  and 
pass  through  some  of  the  masses  of  stai-s  composing  it,  would 
he  find  them  thicker  or  thinner  than  they  are  in  the  visible 
heavens  around  us  ? 

A  question  still  left  open  is,  whether  all  the  celestial  objects 
visible  with  the  telescope  are  included  within  the  limits  of  the 
three  regions  we  have  just  indicated,  or  whether  the  whole 
Galaxy,  with  everything  which  is  included  within  its  limits, 
is  simply  one  of  a  great  number  of  widely  scattered  stellar 
Eystems,  Since  any  consideration  of  invisible  galaxies  and 
systems  would  be  entirely  idle,  the  question  may  be  reduced 
to  this:  Are  the  most  distant  star  clusters  which  the  telescope 
shows  us  situated  within  the  limits  of  the  stellar  system  or  far 
without  them,  a  great  vacant  space  intervening?  The  latter 
alternative  is  the  popular  one,  firet  suggested  by  Kant,  it  be- 
ing supposed  that  the  most  distant  nebulae  constituted  other 
Milky  Ways  or  stellar  systems  as  extensive  as  our  own. 

Although  the  possibility  that  this  view  is  correct  cannot  be 
lenied,  yet  the  arrangement  of  the  star  clusters  or  resolvable 
uebulte  militates  against  it.  We  have  shown  that  the  major- 
ity of  the  latter  lie  near  the  direction  of  the  plane  of  the 
Milky  Way,  comparatively  few  being  seen  near  the  perpen- 
dicular direction.  But  if  these  objects  were  other  galaxies, 
far  outside  of  the  one  which  surrounds  us,  they  would  be  as 
likely  to  lie  in  one  direction  as  in  another,  and  the  probabil- 
ity against  the  great  mass  of  them  lying  in  one  plane  woiild 
be  very  great.  The  most  pi-ububle  conclusion,  therefore,  is 
that  they  constitute  part  of  our  stellar  system.  They  may,  in- 
deed, be  scattered  around  or  outside  of  the  extreme  limits  with- 
in which  single  stars  can  be  seen,  l)Ut  not  at  distances  so  great 
that  they  should  be  considered  as  separate  systems.  The  most 
probable  conclusiun,  in  the  present  state  of  our  knowledge, 


DO  THE  STABS  BEALLY  FOBM  A  SYSTEM?  495 

seems  to  be  that  the  scheme  shown  in  Fig.  Ill  includes  the 
whole  visible  universe. 

The  differences  of  opinion  which  now  exist  respecting  the 
probable  arrangement  and  distance  of  the  stars  arise  mainly 
from  our  uncertainty  as  to  what  is  the  probable  range  of  alj- 
solnte  magnitude  of  the  stars,  a  subject  to  which  we  have  al- 
ready several  times  alluded.  The  discovery  of  the  parallax 
of  several  stars  has  enabled  us  not  only  to  form  some  idea  of 
this  question  by  comparing  the  brilliancy  of  these  stars  with 
their  known  distances,  but  it  has  enabled  us  to  answer  the  in- 
teresting question,  How  does  our  sun  compare  with  these  stars 
in  brightness  'I  The  curious  result  of  this  inquiry  is,  that  our 
sun  is  really  a  star  less  than  the  average,  which  would  mod- 
estly twinkle  among  the  smaller  of  its  fellows  if  removed 
to  the  distance  from  us  at  which  they  are  placed.  ZoUner 
found,  by  comparing  the  light  of  the  sun  with  that  of  Capella, 
or  a  Aurigse,  that  it  would  have  to  be  removed  to  230,000 
times  its  present  distance  to  appear  equally  bright  with  that 
star,  which  we  may  take  as  an  average  star  of  the  first  magni- 
tude. But  the  greater  number  of  the  stars  of  this  magnitude 
are  situated  at  four  or  five  times  this  distance ;  so  that  if  our 
sun  were  placed  at  their  average  distance,  it  would  probably 
not  exceed  the  third  or  fourth  magnitude.  Still,  it  would  by 
no  means  belong  among  the  smallest  stars  of  all,  because  we 
do  find  stars  with  a  measurable  parallax  which  are  only  of 
the  fifth,  sixth,  or  even  the  seventh  magnitude.  Altogether,  it 
appears  that  the  range  of  absolute  brilliancy  among  the  stars 
extends  through  eight  or  ten  magnitudes,  and  tliat  the  largest 
ones  emit  several  t^iousand  times  as  much  light  as  the  small- 
est. It  is  this  range  of  magnitude  which  really  forms  the 
greatest  obstacle  in  the  way  of  determining  the  arrangement 
of  the  stars  in  space. 

§  4.  Do  the  Stars  really  forvi  a  System? 

We  have  described  the  sublime  ideas  of  Kant  and  Lam- 
bert, who,  seeing  the  bodies  of  our  solar  system  fitted  to  go 
through  their  revolutions  without  permanent  change  during 

88 


496  THE  STELLAR   UNIVERSE. 

an  indefinite  period  of  time,  reasoned  by  analogy  that  the 
stellar  universe  was  constructed  on  tlie  same  general  plan, 
and  that  each  star  had  its  appointed  orbit,  round  which  it 
would  run  its  coui-se  during  endless  ages.  This  speculation 
was  not  followed  up  by  Herschel  and  Struve,  who,  proceeding 
on  a  more  strictly  scientific  plan,  found  it  necessary  to  learn 
how  the  stars  are  now  situated  before  attempting  to  decide 
in  what  kinds  of  orbits  they  are  moving.  In  the  absence  of 
exact  knowledge  respecting  the  structure  and  extent  of  the 
stellar  system,  it  is  impossible  to  say  with  certainty  what  will 
be  the  state  of  that  system  after  the  lapse  of  the  millions  of 
years  which  would  be  necessary  for  the  stars  to  perform  a 
revolution  around  one  centre.  But,  as  in  describing  the  con- 
stitution of  the  stellar  system,  we  found  certain  features  on 
wliich  we  could  pronounce  with  a  high  degree  of  probability, 
so,  in  respect  to  the  motions  and  orbits  of  the  stars,  there  are 
some  propositions  which  we  may  sustain  with  a  near  approach 
to  certainty. 

Stability  of  the  System. — We  may  first  assert,  with  a  high  de- 
gree of  probability,  that  the  stars  do  not  form  a  stable  system 
in  the  sense  in  which  we  say  that  the  solar  system  is  stable. 
By  a  stable  system  we  mean  one  in  which  each  star  moves 
round  and  round  in  an  unchanging  orbit,  every  revolution 
bringing  it  back  to  its  starting-point,  so  that  the  system  as  a 
whole  shall  retain  the  same  general  form,  dimensions,  and 
arrangement  during  innumerable  revolutions  of  the  bodies 
which  compose  it.  It  is  almost  necessaiy  to  the  existence  of 
such  a  system  that  it  have  a  great  central  body,  the  mass  of 
which  should  be  at  least  vastly  greater  than  that  of  the  indi- 
vidual bodies  which  revolve  around  it.  At  least,  such  a  cen- 
J;ral  body  could  be  dispensed  with  only  by  the  separate  stars 
having  a  regularity  of  motion  and  arrangement  which  cer- 
tainly does  not  exist  in  the  stellar  system  as  we  actually  Fee 
it.  The  question,  then,  reduces  itself  to  this :  Are  there  any 
immense  attracting  centres  around  which  the  separate  collec- 
tions of  stars  revolve  ;  or  is  there  any  centre  around  which  all 
the  stars  which  compose  the  visible  universe  revolve  ?     In  all 


BO  TEE  STABS  BE  ALLY  FOBM  A  SYSTEM  f  497 

huraau  probability,  these  questions  must  be  answered  in  the 
negative.  All  analogy  leads  us  to  believe  that  if  there  were 
any  such  central  masses,  they  would  be  not  onl}'  larger  than 
the  other  stars,  but  brighter  in  a  yet  greater  proportion.  It 
is,  of  course,  possible  to  conceive  of  immense  dark  bodies, 
such  as  Lambert  supposed  to  exist,  but  we  cannot  but  believe 
tlie  existence  of  such  bodies  to  be  very  improbable.  Al- 
though there  is,  as  we  have  seen,  great  diversity  among  the 
stars  in  respect  to  their  magnitudes,  there  are  none  of  them 
which  seem  to  have  that  commanding  preeminence  above 
their  fellows  wliich  the  sun  presents  above  the  planets  which 
surround  him. 

But  the  most  conclusive  proof  that  the  stars  do  not  revolve 
round  definite  attracting  centres  is  found  in  the  variety  and 
irregularity  of  their  proper  motions,  which  we  have  already 
described.  We  have  shown  (1)  that  when  the  motions  of 
great  numbers  of  stars  are  averaged,  there  is  found  a  general 
preponderance  of  motions  from  the  constellation  Hercules, 
which  is  supposed  to  be  due  to  a  motion  of  our  sun  with  his 
attendant  planets  in  that  direction  ;  and  (2)  that  when  the 
motions  of  stars  in  the  same  region  are  compared,  there  is 
often  found  to  be  a  certain  resemblance  among  them.  But 
this  tendency  towards  a  regular  law  affects  only  large  masses 
of  stars,  and  does  not  imply  any  such  regularity  in  the  mo- 
tions of  individual  stars  as  would  be  apparent  if  they  moved 
in  regular  circular  orbits,  as  the  planets  move  round  the  sun. 
The  motion  of  each  individual  star  is  generally  so  entirely 
different  from  that  of  its  fellows  as  seemingly  to  preclude  all 
reasonable  probability  that  these  bodies  are  revolving  in  defi- 
nite orbits  around  great  centres  of  attraction. 

The  most  extraordinary  instances  of  the  irregularities  of 
which  we  speak  are  found  in  the  stars  of  unusually  rapid 
proper  motion,  which  are  moving  forward  at  such  a  rate  that 
the  gravitation  of  all  the  known  stars  cannot  stop  them  until 
they  shall  have  passed  through  and  beyond  the  visible  uni- 
verse. The  most  remarkable  of  these,  so  far  as  we  know,  is 
Groombridge  1830,  it  having  the  largest  apparent  proper  mo- 


498  THE  STELLAR   UNIVERSE. 

tion  of  any  known  star.  The  most  careful  determinations  of 
its  parallax  seem  to  show  that  its  distance  is  so  immense  that 
the  parallax  is  only  about  a  tenth  of  a  second ;  that  is,  a  line 
drawn  from  the  sun  to  the  earth  would  subtend  an  angle  of 
only  a  tenth  of  a  second  when  viewed  from  this  star.  But 
the  apparent  motion  of  the  star,  as  we  actually  see  it,  is  more 
than  seven  seconds  per  annum,  or  seventy  times  its  parallax. 
It  follows  that  the  star  moves  over  a  space  of  more  than  sev- 
enty times  the  distance  of  the  sun  from  us  in  the  space  of  a 
year.  If,  as  is  likely,  the  motion  of  the  star  is  oblique  to  the 
line  in  which  we  see  it,  its  actual  velocity  must  be  yet  greater. 
Leaving  this  out  of  account,  we  see  that  the  star  would  pass 
from  the  earth  to  the  sun  in  about  five  days,  so  that  its  veloci- 
ty probably  exceeds  two  liundred  miles  per  second. 

To  understand  what  this  enormous  velocity  may  imply,  we 
must  advert  to  the  theorem  of  gravitational  astronomy  that 
the  velocity  which  a  body  can  acquire  by  falling  towards  an 
attracting  centre  is,  at  each,  point  of  its  path,  limited.  For  ex- 
ample, a  body  falling  from  an  infinite  distance  to  the  earth's 
surface,  and  acted  on  by  the  attraction  of  the  earth  alone,  would 
acquire  a  velocity  of  only  about  seven  miles  per  second.  Vice 
versa,  ?i  body  projected  from  the  earth  with  this  velocity  would 
never  be  stopped  by  the  earth's  attraction  alone,  but  would 
describe  an  elliptic  orbit  round  the  sun.  If  the  velocity  ex- 
ceeded twent3'-seven  miles  per  second,  the  attraction  of  the  sun 
himself  could  never  stop  it,  and  it  would  wander  forever 
through  the  stellar  spaces.  The  greater  the  distance  from  the 
sun  at  which  the  body  is  started,  the  less  the  velocity  whicli 
will  thus  carry  it  forever  away  from  the  sun.  At  the  orbit  of 
Uranus  the  required  velocity  would  be  only  six  miles  per  sec- 
ond ;  at  Neptune,  it  would  be  less  than  five  miles  per  second  ; 
half-way  between  the  sun  and  a  Centauri,  it  would  be  a  mile 
in  twelve  seconds,  or  a  fourth  the  speed  of  a  cannon-ball.  If 
we  knew  the  masses  of  each  of  the  stars,  and  their  arrange- 
ment in  space,  it  would  be  easy  to  compute  this  limiting  ve- 
locity for  a  body  falling  from  an  infinite  distance  to  any  point 
of  the  stellar  system.     If  the  motion  of  a  star  were  found  to 


DO   THE  STARS  REALLY  FORM  A  SYSTEM?  499 

exceed  this  limit,  it  would  show  that  the  star  did  not  belong 
to  the  visible  universe  at  all,  but  was  only  a  visitor  flying 
on  a  course  through  infinite  space  at  such  a  rate  that  the 
combined  attraction  of  all  the  stars  could  never  stop  it. 

Let  us  now  see  how  the  case  may  stand  with  our  flying  star, 
and  what  relation  its  velocity  may  bear  to  the  probable  attrac- 
tion of  all  the  stars  which  exist  within  the  range  of  the  tel- 
escope. The  number  of  stars  actually  visible  witli  the  most 
powerful  telescopes  probably  falls  short  of  fifty  millions  ;  but, 
to  take  a  probable  outside  limit,  M'e  shall  suppose  that  within 
the  regions  occupied  by  the  farthest  stars  which  the  telescope 
will  show,  there  are  fifty  millions  more,  so  small  that  we  cannot 
see  them,  making  one  hundred  millions  in  all.  We  shall  also 
suppose  that  these  stars  have,  on  the  avei-age,  five  times  the 
mass  of  tlie  sun,  and  that  they  are  spread  out  in  a  layer  across 
the  diameter  of  which  light  would  require  thirty  thousand  years 
to  pass.  Then,  a  mathematical  computation  of  the  attractive 
power  exerted  by  such  a  system  of  masses  sliows  that  a  body 
falling  from  an  infinite  distance  to  the  centre  of  the  system 
would  acquire  a  velocity  of  twenty -five  miles  per  second. 
Vice  versa,  a  body  projected  from  the  centre  of  such  a  system 
with  a  velocity  of  more  than  twenty-five  miles  per  second  in 
any  direction  whatever  would  not  only  pass  entirely  through 
it,  but  would  fly  off  into  infinite  space,  never  to  return.  If  the 
body  were  anywhere  else  than  in  the  centre  of  the  system,  the 
velocity  necessary  to  carry  it  away  would  be  less  tlian  the 
limit  just  given.  But  this  calculated  limit  is  only  one-eighth 
the  probable  velocity  of  1830  Groombridge.  The  force  re- 
quired to  impress  a  given  velocity  on  a  body  falling  tlu-ough 
any  distance  is  proportional  to  the  square  of  the  velocity,  four 
times  the  force  being  required  to  give  double  the  velocity,  nine 
times  to  increase  it  threefold,  and  so  on.  To  give  eight  times 
the  velocity  would  require  sixty-four  times  the  attracting  mass. 
If,  then,  the  star  in  question  belongs  to  our  stellar  system,  the 
masses  or  extent  of  that  system  must  be  many  times  greater 
than  telescopic  observation  and  astronomical  research  indicate. 
We  may  place  the  dilemma  in  a  concise  form,  as  follows : 


500  THE  STELLAR   UNIVERSE. 

Either  the  bodies  which  compose  onr  universe  are  vastlj' 
more  massive  and  numerous  than  telescopic  examination 
seems  to  indicate,  or  1830  Groorabridge  is  a  runaway  star, 
flving  on  a  boundless  course  through  infinite  space  with  such 
momentum  that  the  attraction  of  all  the  bodies  of  the  univei'se 
can  never  stop  it. 

Which  of  these  is  the  more  probable  alternative  we  cannot 
pretend  to  say.  That  the  star  can  neither  be  stopped,  nor  bent 
far  from  its  course  until  it  has  passed  the  extreme  limit  to 
which  the  telescope  has  ever  penetrated,  we  may  consider 
reasonably  certain.  To  do  this  will  require  two  or  three  mill- 
ions of  years.  Whether  it  will  then  be  acted  on  by  attractive 
forces  of  which  science  has  no  knowledge,  and  thus  carried 
back  to  where  it  started,  or  whether  it  will  continue  straight 
forward  forever,  it  is  impossible  to  say. 

Much  the  same  dilemma  may  be  applied  to  the  past  history 
of  this  body.  If  the  velocity  of  two  hundred  miles  or  more 
per  second  with  which  it  is  moving  exceeds  any  that  could  be 
produced  by  the  attraction  of  all  the  other  bodies  in  the  uni- 
vei'se,  then  it  must  have  been  flying  forward  through  space 
from  the  beginning,  and,  having  come  from  an  infinite  dis- 
tance, must  be  now  passing  through  our  system  for  the  first 
and  only  time. 

It  may  be  asked  whether,  in  Lambert's  hypothesis  of  im- 
mense attracting  bodies,  invisible  on  account  of  their  being 
dark,  we  have  not  at  once  the  centres  required  to  give  general 
stability  to  the  stellar  system,  and  to  keep  the  star  of  which 
we  have  spoken  in  some  regular  orbit.  We  answer,  no.  To 
secure  such  stability,  stai*s  equally  distant  from  the  attracting 
centres  must  move  with  nearly  the  same  velocity.  An  at- 
tracting centre  sufficiently  powerful  to  bring  a  body  moving 
two  hundred  miles  ])er  second  into  a  regular  orbit  would 
draw  most  of  the  other  stars  moving  with  small  velocities  into 
its  immediate  neighborhood,  and  thus  subvert  the  system.  We 
thus  meet  the  double  difficulty  that  we  have  good  reason  to 
doubt  the  existence  of  these  opaque,  dark  bodies,  and  that  if 
they  did  exist,  they  would  not  fulfil  our  requirements. 


DO  THE  STABS  BE  ALLY  FOBM  A  SYSTEM?  501 

The  general  result  of  our  inquiry  is  that  the  stellar  uni- 
verse does  not  seem  to  possess  that  form  of  unvarying  stabil- 
ity which  we  see  in  tlie  solar  system,  and  that  the  stars  move 
in  irregular  courses  depending  on  their  situation  in  respect 
to  the  surrounding  stars,  and  probably  changing  as  this  situa- 
tion changes.  If  there  were  no  motion  at  all  among  the  stars, 
they  would  all  fall  to  a  common  centre,  and  universal  ruin 
would  be  the  result.  But  the  motions  which  we  actually  see 
are  sufficient  to  prevent  this  catastrophe,  by  supplying  each 
star  with  a  reserve  of  force  which  will  generally  keep  it  from 
actual  collision  with  its  neighbors.  If,  then,  any  one  star 
does  fall  towards  any  attracting  centre,  the  velocity  which  it 
acquires  by  this  fall  will  carry  it  away  again  in  some  other 
direction,  and  thus  it  may  keep  up  a  continuous  dance,  under 
the  influence  of  ever-varying  forces,  as  long  as  the  universe 
shall  exist  under  its  present  form. 

To  those  who  have  been  enraptured  with  the  sublime  specu- 
lations of  Kant  and  Lambert,  this  may  seem  an  unsatisfactory 
conclusion;  while  to  those  who  look  upon  the  material  uni- 
verse as  something  made  to  last  forever,  it  may  seem  improba- 
ble. But  when  we  consider  the  immense  periods  which  would 
be  reauired  for  the  mutual  gravitation  of  the  stars  to  effect 
any  great  change  in  the  stellar  system,  we  may  be  led  to  alter 
such  views  as  these.  We  have  shown  that  tens  of  thousands 
of  years  would  be  required  to  make  any  great  change  in  the 
arrangement  of  tlie  stars  which  we  see  Avith  the  naked  eye. 
The  time  required  for  all  the  stars  visible  witli  the  telescope 
to  fall  together  by  their  own  attraction  is  to  be  counted  by 
millions  of  years.  If  the  universe  had  existed  in  its  present 
state  from  eternity,  and  were  to  exist  forever,  the  immensity 
of  these  periods  would  not  be  at  all  to  the  point,  because  a 
million  of  years  is  no  more  a  part  of  eternity  than  a  single 
day.  But  all  modern  science  seems  to  point  to  the  finite 
duration  of  our  system  in  its  present  form,  and  to  carry  us 
back  to  the  time  when  neither  sun  nor  planet  existed,  save  as 
a  mass  of  glowing  gas.  How  far  back  that  was,  it  cannot  tell 
us  with  certainty ;  it  can  only  say  that  the  period  is  counted 


503  THE  STELLAB   UNIVEESE. 

by  millions  of  year?,  but  probably  not  by  hundreds  of  mill- 
ions. It  also  points  forward  to  the  time  when  the  sun  and 
stars  shall  fade  away,  and  nature  shall  be  enshrouded  in  dark- 
ness and  death,  unless  some  power  now  unseen  shall  uphold 
or  restore  her.  The  time  required  for  this  catastrophe  cannot 
be  calculated ;  but  it  is  probably  not  so  great  that  the  stellar 
system  can,  in  the  mean  time,  be  subverted  by  the  mutual 
gravitation  of  its  members. 

It  would  thus  appear  as  if  those  nicely  arranged  adjust- 
ments which  secure  stabiHty  and  uniformity  of  motion  are 
not  found  where  they  are  not  necessary  to  secure  the  system 
from  subversion  during  the  time  it  is  to  last,  much  as  the 
wheel  of  an  engine  which  is  to  make  but  two  or  three  revo- 
lutions while  the  engine  endures  need  not  be  adjusted  to 
make  thousauds  of  revolutions.  The  bodies  which  form  our 
solar  system  are,  on  the  other  hand,  like  wlieels  which  have 
to  make  millions  of  revolutions  before  they  stop.  Unless  there 
is  a  constant  balance  between  the  opposing  forces  under  the 
influence  of  which  they  move,  there  must  be  a  disarrangement 
of  the  movement  long  before  the  engine  wears  out.  Thus, 
although  the  present  arrangement  of  the  stars  may  be  studied 
without  any  reference  to  their  origin,  yet,  M'hen  we  seek  to 
penetrate  the  laws  of  their  motion,  and  foresee  the  changes 
of  state  to  which  their  motions  may  give  rise,  we  ai-e  brought 
to  face  the  question  of  their  duration,  and  hence  of  their  be- 
giuuing  and  end. 


THE  COSMOGONY.  503 


CHAPTER  III. 


THE     COSMOGONY. 


The  idea  that  the  world  has  not  endured  forever  in  the 
form  in  which  we  now  see  it,  but  that  there  was  a  time  when 
it  either  did  not  exist  at  all,  or  existed  only  as  a  mass  "with- 
out form,  and  void,"  is  one  which  we  find  to  have  been  always 
held  by  mankind.  The  "  chaos"  of  the  Greeks — the  rude  and 
formless  materials,  subject  to  no  law,  out  of  which  all  things 
were  formed  by  the  creative  power— corresponds  in  a  striking 
manner  to  the  nebulous  masses  of  modern  astronomy.  These 
old  ideas  of  chaos  were  expressed  by  Milton  in  the  second 
book  of  '•  Paradise  Lost,"  before  such  a  thing  as  a  nebula 
could  be  said  to  be  known,  and  he  would  be  a  bold  astrono- 
mer who,  in  giving  a  description  of  the  primeval  nebulous 
mass,  would  attempt  to  improve  on  the  great  poet : 

"  ti  dark, 

Illimitable  ocean,  without  bound, 

AVithout  dimension,  where  length,  breadth,  and  height, 

And  time  and  place,  are  lost ;  where  eldest  Night 

And  Chaos,  ancestors  of  Nature,  hold 

Eternal  anarchy  amidst  the  noise 

Of  endless  wars,  and  by  confusion  stand  : 

For  hot,  cold,  moist,  and  dry,  four  champions  fierce, 

Strive  here  for  mastery,  and  to  battle  bring" 

Their  embryon  atoms. 

*  *  !):  «  «  «  « 

Chaos  umpire  sits, 
And  by  decision  more  embroils  the  fray 
By  which  he  reigns  :  next  him,  high  arbiter, 
Chance  governs  all.     Into  this  wild  abyss 
The  womb  of  Nature,  and  perhaps  her  grave, 
Of  neither  sea,  nor  shore,  nor  air,  nor  fire, 
But  all  these  in  their  pregnant  causes  mixed 
Confusedly,  and  which  thus  must  ever  fight. 


504:  THE  STELLAR   UNIVERSE. 

Unless  the  almighty  Maker  them  ordain 
His  dark  materials  to  create  more  worlds — 
****** 

Some  tumultuous  cloud 
Instinct  with  fire  and  nitre." 

If  wc  classify  men's  ideas  of  the  cosmogony  according  to 
the  data  on  which  tliey  are  founded,  we  shall  find  theni  divis- 
ible into  three  classes.  The  first  class  comprises  those  formed 
before  the  discovery  of  the  theory  of  gravitation,  and  M-hich, 
for  this  reason,  however  correct  they  might  have  been,  had  no 
really  scientific  foundation.  The  Second  are  those  founded  on 
the  doctrine  of  gravitation,  but  without  a  knowledge  of  the 
modern  theory  of  the  conservation  of  force ;  while  the  third 
are  founded  on  this  theory.  It  must  not  be  supposed,  how- 
ever, tliat  the  ideas  of  the  last-mentioned  class  are  antagonistic 
to  those  of  the  other  classes.  Kant  and  Laplace  founded  the 
nebular  hypothesis  on  the  theory  of  gravitation  alone,  the  con- 
servation of  force  being  then  entirely  unknown.  It  was,  there- 
fore, incomplete  as  it  came  from  their  hands,  but  not  neces- 
sarily erroneous  in  its  fundamental  conceptions. 

The  consideration  of  the  ancient  ideas  of  the  origin  of  the 
world  belongs  rather  to  the  history  of  philosophy  than  to  as- 
tronomy, for  the  reason  that  they  were  of  necessity  purely 
speculative,  and  reflected  rather  the  mode  of  thought  of  the 
minds  in  which  they  originated  than  any  definite  system  of 
investigating  the  operations  of  nature.  The  Hindoo  concep- 
tion of  Bralnna  sitting  in  meditation  on  a  lotus-leaf  through 
long  ages,  and  then  producing  a  golden  eg^  as  large  as  the 
universe,  out  of  which  the  latter  was  slowly  evolved,  is  not 
founded  on  even  the  crudest  observation,  but  is  purely  a  result 
of  the  speculative  tendency  of  the  Hindoo  mind.  Tlie  Jew- 
ish cosmogony  is  the  expression  of  the  monotheistic  views  of 
that  people,  and  of  the  identity  of  their  tutelary  divinity  with 
the  maker  of  heaven  and  earth.  Hipparchus  and  Ptolemy 
showed  the  scientific  turn  of  their  minds  by  confining  them- 
selves to  the  examination  of  the  universe  as  it  is,  without  mak« 
ing  any  vain  effort  to  trace  its  origin. 


THE  MODERN  NEBULAR  HYPOTHESIS.  505 

Thougli  the  systems  to  which  we  refer  are  essentially  un- 
scientific, it  must  not  be  supposed  that  they  were  all  errone- 
ous in  their  results,  or  that  they  belong  exclusively  to  ancient 
times.  Thus,  the  views  of  Swedenborg,  though  they  belong 
to  the  class  in  question,  are  remarkably  in  accordance  with 
recent  views  of  the  subject  as  regards  the  actual  changes  which 
took  place  during  the  formation  of  the  planets.  A  great  deal 
of  what  is  written  on  the  subject  at  present  is  to  be  included 
in  this  same  ancient  class,  as  being  the  production  of  men  who 
are  not  mathematicians  or  working  astronomers,  and  who, 
therefore,  cannot  judge  whether  their  views  are  in  accordance 
with  mechanical  laws  and  with  the  facts  of  observation.  Pass- 
ing over  all  speculation  of  this  sort,  no  matter  Avlien  or  by 
whom  produced,  we  shall  consider  in  historical  order  the  works 
of  those  who  have  actually  contributed  to  placing  the  laws  of 
cosmogony  on  a  scientific  foundation. 

§  1.   The  Modern  Nebular  Hypothesis. 

From  a  purely  scientific  point  of  view,  Kant  has  probably 
the  best  right  to  be  regarded  as  the  founder  of  the  nebular 
hypothesis,  because  he  based  it  on  an  examination  of  the  actual 
features  of  the  solar  system,  and  on  the  Newtonian  doctrine 
of  the  mutual  gravitation  of  all  matter.  His  reasoning  is 
briefly  this:  Examining  the  solar  system,  we  find  two  remark- 
able features  presented  to  our  consideration.  One  is  that  six 
planets  and  nine  satellites  (the  entire  number  then  known) 
move  around  the  sun  in  circles,  not  only  in  the  same  direction 
in  which  the  sun  himself  revolves  on  his  axis,  but  very  nearly 
in  the  same  plane.  This  common  feature  of  the  nu)tion  of 
so  many  bodies  could  not,  by  any  reasonable  possibility,  have 
been  a  result  of  chance;  we  are,  therefore,  forced  to  believe 
that  it  must  be  the  result  of  some  common  cause  originally 
acting  on  all  the  planets. 

On  the  other  hand,  when  we  consider  the  spaces  in  which 
the  planets  move,  we  find  them  entirely  void,  or  as  good  as 
void;  for  if  there  is  any  matter  in  them, it  is  so  rare  as  to  be 
without  effect  on  the  planetary  motions.     There  is,  thereforCj 


506 


THE  STELLAR    UXLVEESE. 


no  material  connection  now  existing  between  the  planets 
throufijh  which  they  might  have  been  forced  to  take  up  a  com- 
mon direction  of  motion.  How,  then,  are  we  to  reconcile  this 
common  motion  with  the  absence  of  all  material  connection  ? 
The  most  natm*al  way  is  to  suppose  that  there  was  once  some 
such  connection  which  brought  about  the  uniformity  of  mo- 
tion which  we  observe  ;  that  the  materials  of  which  the  plan- 
ets are  formed  once  filled  the  whole  space  between  them.  "  I 
assume,"  says  Kant, "  that  all  the  materials  out  of  which  the 
bodies  of  our  solar  system  M'ere  formed  were,  in  the  begin- 
ning of  things,  resolved  in  their  original  elements,  and  filled  all 
the  space  of  the  univei-se  in  which  these  bodies  now  move.'' 
There  was  no  formation  in  this  chaos,  the  formation  of  sepa- 
rate bodies  by  the  mutual  gravitation  of  parts  of  the  mass  be- 
ing a  later  occurrence.  But,  naturally,  some  parts  of  the  mass 
would  be  more  dense  than  others,  and  would  thus  gather 
around  them  the  rare  matter  which  filled  the  intervening 
spaces.  The  larger  collections  thus  formed  would  draw  the 
smaller  ones  into  them,  and  this  process  would  continue  until 
a  few  round  bodies  had  taken  the  place  of  the  original  chaotic 
mass. 

If  we  examine  the  result  of  this  hypothesis  by  the  light  of 
modern  science,  we  shall  readily  see  that  all  the  bodies  thus 
formed  would  be  drawn  to  a  common  centre,  and  thus  we 
should  have,  not  a  collection  of  bodies  like  the  solar  system, 
but  a  single  sun  formed  by  the  combination  of  them  all.  In 
attempting  to  show  how  the  smaller  masses  would  be  led  to 
circulate  aiound  the  larger  ones  in  circular  orbits,  Kant's  rea- 
soning ceases  to  be  satisfactory.  He  seems  to  think  that  the 
motion  of  rotation  could  be  produced  indirectly  by  the  repul- 
sive forces  acting  among  the  rarer  masses  of  the  condensing 
matter,  which  would  give  rise  to  a  M-hirling  motion.  But  the 
laws  of  mechanics  show  that  the  sum  total  of  rotary  motion  in 
a  system  can  never  be  increased  or  diminished  by  the  mutual 
action  of  its  separate  parts,  so  that  the  present  rotary  motions 
of  the  sun  and  planets  must  be  the  equivalent  of  that  which 
they  had  from  the  beginning. 


THE  MODEBN  NEBULAR  HYPOTHESIS.  507 

HerscheVs  Hypothesis.  —  It  is  remarkable  that  the  idea  of 
the  gradual  transmutation  of  nebulae  into  stars  seems  to  have 
been  suggested  to  Herschel,  not  by  the  relations  of  the  solar 
system,  but  by  his  examinations  of  the  nebulse  themselves. 
Many  of  these  bodies  seemed  to  him  to  be  composed  of  im- 
mense masses  of  phosphorescent  vapor,  and  he  conceived  that 
these  masses  must  be  gradually  condensing,  each  around  its 
own  centre,  or  around  those  parts  where  it  is  most  dense,  until 
it  should  be  transmuted  into  a  star  or  a  cluster  of  stars.  On 
classifying  the  numerous  nebulae  which  he  discovered,  it 
seemed  to  him  that  lie  could  see  each  stage  of  this  operation 
going  on  before  his  eyes.  There  were  the  large,  faint,  diffused 
nebulae,  in  which  the  process  of  condensation  seemed  to  have 
hardly  begun ;  the  smaller  but  brighter  ones,  which  had  been 
so  far  condensed  that  the  central  parts  would  soon  begin  to 
form  into  stars  ;  yet  others,  in  which  stars  had  actually  begun 
to  form  ;  and,  finally,  star  clusters  in  which  the  condensation 
was  complete.  As  Laplace  observes,  Herschel  followed  the 
condensation  of  the  nebulae  in  much  the  same  way  that  we 
can,  in  a  forest,  study  the  growth  of  the  trees  by  comparing 
those  of  the  different  ages  which  the  forest  contains  at  the 
same  time.  The  spectroscopic  revelations  of  the  gaseous  nat- 
ure of  the  true  nebulae  tend  to  strengthen  these  views  of  Her- 
schel, and  to  confirm  us  in  the  opinion  that  these  masses  will 
all  at  some  time  condense  into  stars  or  clusters  of  stars. 

Laplace  s  View  of  the  Nebular  Hypothesis. — Laplace  was  led 
to  the  nebular  hypothesis  by  considerations  very  similar  to 
those  presented  by  Kant  a  few  years  before.  The  remarkable 
uniformity  among  the  directions  of  rotation  of  the  planets  be- 
ing something  which  could  not  have  been  the  result  of  chance, 
he  sought  to  investigate  its  probable  cause.  This  cause,  he 
thought,  could  be  nothing  else  than  the  atmosphere  of  the  sun, 
which  once  extended  so  far  out  as  to  fill  all  the  space  now  oc- 
cupied by  the  planets.  He  does  not,  like  Kant,  begin  with  a 
chaos,  out  of  which  order  was  slowly  evolved  by  the  play  of 
attractive  and  repulsive  forces,  but  with  the  sun,  surrounded 
by  this  immense  fiery  atmosphere.     Knowing,  from  median- 


508  THE  STELLAR   VXIVEESE. 

ical  laws,  that  the  sum  total  of  rotary  motion  now  seen  in  the 
planetary  system  must  have  been  there  from  the  beginning,  he 
conceives  the  immense  vaporous  mass  forming  the  sun  and 
his  atmosphere  to  have  had  a  slow  rotation  on  its  axis.  The 
mass  being  intensely  hot  would  slowly  cool  off,  and  as  it  did  so 
would  contract  toM'ards  the  centre.  As  it  contracted,  its  ve- 
locity of  rotation  would,  in  obedience  to  one  of  the  funda- 
mental laws  of  mechanics,  constantly  increase,  so  that  a  time 
would  arrive  when,  at  the  outer  boundary  of  the  mass,  the  cen- 
trifugal force  due  to  the  rotation  would  counterbalance  the  at- 
tractive force  of  the  central  mass.  Then,  those  outer  portions 
would  be  left  behind  as  a  revolving  ring,  while  the  next  inner 
portions  would  continue  to  contract  until,  at  their  boundary, 
the  centrifugal  and  attractive  forces  would  be  again  balanced, 
when  a  second  ring  would  be  left  behind,  and  so  on.  Thus, 
instead  of  a  continuous  atmosphere,  the  sun  would  be  sur- 
rounded by  a  series  of  concentric  revolving  rings  of  vapor. 

Xow,  how  would  these  rings  of  vapor  behave  ?  As  they 
cooled  off,  their  denser  materials  would  condense  first,  and 
thus  the  ring  would  be  composed  of  a  mixed  mass,  partly  solid 
and  parti}'  vaperous,  the  quantity  of  solid  matter  constantly 
increasing,  and  that  of  vapor  diminishing.  If  the  ring  were 
perfectly  uniform,  this  condensing  process  would  take  place 
equally  all  around  it,  and  the  ring  would  thus  be  broken  up 
into  a  group  of  small  planets,  like  that  which  we  see  between 
Mars  and  Jupiter.  But  we  should  expect  that  in  general 
some  portions  of  the  ring  would  be  much  denser  than  others, 
and  the  denser  portions  would  gradually  attract  the  rarer  por- 
tions around  it  until,  instead  of  a  ring,  we  should  have  a  sin- 
gle mass,  composed  of  a  nearly  solid  centre  surrounded  by  an 
immense  atmosphere  of  fiery  vapor.  Tliis  condensation  of  the 
ring  of  vapor  around  a  single  point  would  have  produced  no 
change  in  the  amount  of  rotary  motion  originally  existing  in 
the  ring  ;  the  planet,  surrounded  by  its  fiery  atmosphere,  would 
therefore  be  in  rotation,  and  would  be,  in  miniature,  a  repro- 
duction of  the  case  of  the  sun  surrounded  by  his  atmosphere 
with  which  we  set  out.     In  the  same  wav  that  the  solar  at- 


THE  MODERN  NEBULAR  HYPOTHESIS.  509 

mosphere  formed  itself  first  into  rings,  and  then  these  rings 
condensed  into  planets,  so,  if  the  planetary  atmospheres  were 
sufficiently  extensive,  they  would  form  themselves  into  rings, 
and  these  rings  would  condense  into  satellites.  In  the  case  of 
Saturn,  however,  one  of  the  rings  was  so  perfectly  uniform 
that  there  could  be  no  denser  portion  to  draw  the  rest  of 
the  ring  around  it,  and  thus  we  have  the  well  -  known  rings 
of  Saturn. 

If,  among  the  materials  of  the  solar  atmosphere,  there  were 
any  so  rare  and  volatile  that  tliey  w^ould  not  unite  themselves 
either  into  a  ring  or  around  a  planet,  they  would  continue  to 
revolve  around  the  sun,  presenting  an  appearance  like  that 
of  the  zodiacal  light.  They  would  offer  no  appreciable  re- 
sistance to  the  motion  of  the  planets,  not  only  on  account  of 
their  extreme  rarity,  but  because  their  motion  would  be  the 
same  as  that  of  the  planets  which  move  among  tliem. 

Such  is  the  celebrated  nebular  hypothesis  of  Laplace  which 
has  given  rise  to  so  much  discussion.  It  commences,  not  with 
a  purely  nebulous  mass,  but  with  the  sun  surrounded  by  a 
fiery  atmosphere,  out  of  which  the  planets  were  formed.  On 
this  theory  the  sun  is  older  than  the  planets ;  otherwise  it 
would  have  been  imjDossible  to  account  for  the  slow  rotation 
of  the  sun  upon  his  axis.  If  his  body  had  been  formed  of  ho- 
mogeneous matter  extending  out  uniformly  to  near  the  orbit 
of  Mercury,  it  would  not  have  condensed  into  a  globe  revolv- 
ing on  its  axis  in  twenty-five  days,  but  into  a  flat,  almost  lens- 
shaped,  body,  which  would  have  been  kept  from  forming  a 
sphere  by  the  centrifugal  force.  But  the  denser  materials  be- 
ing condensed  first,  perhaps  into  such  a  body  as  we  described, 
the  friction  of  the  uncondensed  atmosphere  would  liave  di- 
minished the  rotation  of  the  sun,  the  rotating  enei-gy  which  he 
lost  being  communicated  to  the  embrj-o  planets  and  throwing 
them  farther  away. 

In  accordance  with  the  hypothesis  of  Laplace,  it  has  al- 
ways been  supposed  that  the  outer  planets  were  formed  first. 
There  is,  hoM-ever,  a  weak  point  in  Laplace's  theory  of  the  for- 
mation of  rings.     He  supposed  that  when  the  centrifugal  and 


510  THE  STELLAR   UNIVERSE. 

centripetal  forces  balanced  each  other  at  the  outer  limit  of 
the  revolving  mass,  the  outer  portions  were  separated  from  the 
rest,  M-hich  continued  to  drop  towards  the  centre.  If  the  plan- 
etary rings  were  formed  in  this  way,  then,  after  each  ring  was 
thrown  off,  the  atmosphere  must  have  condensed  to  nearly 
half  its  diameter  before  another  would  have  been  thrown  off, 
because  we  see  that  each  planet  is,  on  the  whole,  nearly  twice 
as  far  as  the  one  next  within  it.  But  there  being  no  cohe- 
sion between  particles  of  vapor,  such  thro  wing-off  of  immense 
masses  of  the  outside  portions  of  the  revolving  mass  was  im- 
possible. The  moment  the  forces  balanced,  the  outer  portions 
of  the  mass  would,  indeed,  cease  to  drop  towards  the  sun,  and 
would  partially  separate  from  the  portions  next  to  it ;  then 
these  would  separate  next,  and  so  on  ;  that  is,  there  would  be 
a  constant  dropping-off  of  matter  from  the  outer  portions,  so 
that,  instead  of  a  series  of  rings,  there  would  have  been  a  flat 
disk  formed  of  an  infinite  number  of  concentrating  rings  all 
joined  together. 

If  we  examine  the  subject  more  closely,  we  shall  see  that 
the  whole  reasoning  by  which  it  is  supposed  that  the  inner 
portions  of  the  mass  would  drop  away  from  the  outer  ones 
needs  important  modifications.  In  its  primeval  state,  when  it 
extended  far  beyond  the  present  confines  of  the  solar  system, 
the  rare  nebulous  atmosphere  must  have  been  nearly  spherical. 
As  it  gradually  contracted,  and  the  effect  of  centrifugal  force 
thus  became  more  marked,  it  would  have  assumed  the  form 
of  an  oblate  spheroid.  "When  the  contraction  had  gone  so 
far  that  tlie  centrifugal  and  attracting  forces  nearly  balanced 
each  other  at  the  onter  equatorial  limit  of  the  mass,  tlie  result 
would  have  been  that  contraction  in  the  direction  of  the  equa- 
tor would  cease  entirely,  and  be  confined  to  the  polar  regions, 
each  particle  dropping,  not  towards  the  sun,  but  towards  the 
])lane  of  the  solar  equator.  Thus,  we  should  have  a  constant 
flattening  of  tlie  spheroidal  atmosphere  until  it  was  reduced 
to  a  thin  flat  disk.  This  disk  might  then  separate  itself  into 
rings,  which  would  form  planets  in  much  the  same  wa}'  that 
Laplace  supposed.     But  there  would  probably  be  no  marked 


FBOGRESSIVE  CHANGES  IN  OUli  SYSTEM.  oU 

difference  in  the  age  of  the  planets ;  quite  likely  tlie  smaller 
inner  rings  would  condense  into  planets  more  rapidly  than  the 
wide-spread  outer  ones. 

Kant  and  Laplace  may  be  said  to  have  arrived  at  the  neb- 
ular hypothesis  by  reasoning  forward,  and  showing  how,  by 
supposing  that  the  space  now  occupied  by  the  solar  system 
was  once  filled  by  a  chaotic  or  vaporous  mass,  from  which  the 
planets  were  formed,  the  features  presented  by  this  system 
could  be  accounted  for.  We  are  now  to  show  how  our  mod- 
ern science  reaches  a  similar  result  by  reasoning  backward 
from  actions  which  we  see  going  on  before  our  eyes. 

§  2.  Progressive  Changes  in  our  System. 

During  the  short  period  within  which  accurate  obsei'vations 
liave  been  made,  no  actual  permanent  change  has  been  ob- 
served in  our  system.  The  earth,  sun,  and  planets  remain  of 
the  same  magnitude,  and  present  the  same  appearance  as  al- 
ways. The  stars  retain  their  brilliancy,  and,  for  the  most  part, 
the  nebulae  their  form.  INot  the  slightest  variation  has  been 
detected  in  the  amount  of  heat  received  from  the  sun,  or  in 
the  average  number  and  extent  of  the  spots  on  his  surface. 
And  yet  we  have  reason  to  believe  that  these  things  are  all 
changing,  and  tliat  the  time  will  come  when  the  state  of  the 
universe  will  be  very  different  from  that  in  which  we  now  see 
it.  How  a  change  may  be  inferred  when  none  is  actually  vis- 
ible may  be  shown  by  a  simple  example. 

Suppose  an  inquiring  person,  walking  in  what  he  sup- 
posed to  be  a  deserted  building,  to  find  a  clock  running.  If 
he  is  ignorant  of  mechanics,  he  will  see  no  reason  why  it  may 
not  have  been  running  just  as  he  now  sees  it  for  an  indefinite 
period,  and  why  the  pendulum  may  not  continue  to  vibiate, 
and  the  hands  to  go  through  their  revolutions,  so  long  as  the 
fabric  shall  stand.  lie  sees  a  continuous  cycle  of  motions,  and 
can  give  no  reason  why  they  should  not  have  been  going  on 
since  the  clock  was  erected,  and  continue  to  go  on  till  it  shall 
decay.     But  let  him  be  instructed  in  the  laws  of  mechanics, 

and  let  him  inquire  into  the  force  which  keeps  the  liands  and 
Z  3i 


512  THE  STELLAR   UNIVERSE. 

pendulum  in  motion.  He  -will  then  find  that  this  force  is 
transmitted  to  the  pendulum  through  a  train  of  wheels,  each 
of  which  moves  many  times  slower  than  that  in  front  of  it, 
and  that  the  first  wheel  is  acted  upon  by  a  weight,  with  which 
it  is  connected  by  a  cord.  He  can  see  a  slow  motion  in  the 
wheel  which  acts  on  the  pendulum,  and  perhaps  in  the  one 
next  behind  it,  while  during  the  short  time  he  has  for  exami- 
nation he  can  see  no  motion  in  the  others.  But  if  he  sees  how 
the  wheels  act  on  each  other,  he  will  know  that  they  must  all 
be  in  motion ;  and  when  he  traces  the  motion  back  to  the  first 
wheel,  he  sees  that  its  motion  must  be  kept  up  by  a  gradual 
falling  of  the  weight,  though  it  seems  to  remain  in  the  same 
position.  He  can  then  say  with  entire  certainty:  "I  do  not  see 
this  weight  move,  but  I  know  it  must  be  gradually  approach- 
ing the  bottom,  because  I  see  a  system  of  moving  machinery, 
the  progress  of  whicli  necessarily  involves  such  a  slow  falling 
of  the  weight.  Knowing  the  number  of  teeth  in  each  wheel 
and  pinion,  I  can  compute  how  man}'  inches  it  falls  eacli  day; 
and  seeing  how  mucli  room  it  has  to  fall  in,  I  can  tell  how 
many  days  it  will  take  to  reach  the  bottom.  When  this  is 
done,  I  see  that  the  clock  must  stop,  because  it  is  only  the  fall- 
ing of  the  weight  that  keeps  its  pendulum  in  motion.  More- 
over, I  see  that  the  weight  must  have  been  higher  yesterday 
than  it  is  to-day,  and  yet  higher  the  day  before,  so  that  I  can 
calculate  its  position  backward  as  well  as  forward.  By  this 
calculation  I  see  backward  to  a  time  when  the  weight  was 
at  the  top  of  its  coui'se,  higher  than  which  it  could  not  be. 
Thus,  althougli  I  see  no  motion,  I  see  with  the  eye  of  reason 
that  the  weight  is  running  througli  a  certain  course  from  the 
top  of  the  clock  to  the  bottom ;  that  some  power  must  have 
wound  it  up  and  started  it ;  and  that  unless  the  same  power 
intervenes  again,  the  weight  must  reach  the  bottom  in  a  cer- 
tain number  of  days,  and  the  clock  must  then  stop." 

The  corresponding  progressive  change  exhibited  by  the 
operations  of  nature  consists  in  a  constant  transformation  of 
motion  into  heat,  and  the  constant  loss  of  that  heat  by  radia- 
tion into  space.     As  Sir  "William  Thomson  has  expressed  it, 


rr.OGEESSIVE  CHANGES  IN  OUR  SYSTEM.  513 

a  constant  "dissipation  of  energy"  is  going  on  in  nature. 
We  all  know  that  the  sun  has  been  radiating  heat  into  space 
during  the  whole  course  of  his  existence.  A  small  portion  of 
this  heat  strikes  the  earth,  and  supports  life  and  motion  on  its 
surface.  All  this  portion  of  the  snn's  heat,  after  performing 
its  function,  is  radiated  off  into  space  by  the  earth  itself.  The 
portion  of  the  sun's  radiant  heat  received  by  the  earth  is,  how- 
ever, comparatively  insignificant,  since  our  luminary  radiates 
in  every  direction  equally,  while  the  earth  can  receive  only  a 
part  represented  by  the  ratio  which  its  apparent  angular  mag- 
nitude as  seen  from  the  sun  bears  to  the  whole  celestial  sphere, 
which  a  simple  calculation  shows  to  be  the  ratio  of  1  to 
2,170,000,000.  The  stars  radiate  heat  as  well  as  the  sun. 
The  heat  received  from  them,  when  condensed  in  the  focus  of 
a  telescope,  has  been  rendered  sensible  by  the  thermo-multi- 
plier,  and  there  is  every  reason  to  believe  that  stellar  heat  and 
light  bear  the  same  proportion  to  each  other  that  solar  heat 
and  light  do.  Wherever  there  is  white  stellar  light,  there 
must  be  stellar  heat ;  and  as  we  have  found  that  the  stars  in 
general  give  more  light  than  the  sun,  we  have  reason  to  be- 
lieve that  they  give  more  heat  also.  Thus  we  have  a  contin- 
uous radiation  from  all  the  visible  bodies  of  the  universe, 
which  must  have  been  going  on  from  the  beginning. 

Until  quite  recently,  it  was  not  known  that  this  radiation 
involved  the  expenditure  of  a  something  necessarily  limited  in 
supply,  and,  consequently,  it  was  not  known  but  that  it  might 
continue  forever  without  any  loss  of  power  on  the  part  of  tlie 
sun  and  stars.  But  it  is  now  known  that  heat  cannot  be  pro- 
duced except  by  the  expenditure  of  force,  actual  or  potential, 
in  some  of  its  forms,  and  it  is  also  known  that  the  available 
supply  of  force  is  necessarily  limited.  One  of  the  best-estab- 
lished doctrines  of  modern  science  is  that  force  can  no  more 
be  produced  from  nothing  than  matter  can:  to  find  it  so  pro- 
duced would  be  as  complete  a  miracle  as  to  see  a  globe  created 
from  nothing  before  our  eyes.  Hence,  this  radiation  cannot 
go  on  forever  unless  the  force  expended  in  producing  the  heat 
be  returned  to  the  sun  in  some  form.     That  it  is  not  now 


514  THE  STELLAR   UNIVERSE. 

60  returned  we  may  regard  as  morally  certain.  There  is  no 
known  law  of  radiation,  except  that  it  proceeds  out  in  straight 
lines  fi-om  the  radiating  centre.  If  the  heat  were  returned 
back  to  the  sun  from  space,  it  would  have  to  return  to  the 
centre  from  all  directions ;  the  earth  would  then  intercept  as 
much  of  the  incoming  as  of  the  outgoing  heat ;  that  is,  we 
should  receive  as  much  heat  from  the  sky  at  night  as  from 
the  sun  by  day.  We  know  very  well  that  this  is  not  the  case ; 
indeed,  there  is  no  evidence  of  any  heat  at  all  reaching  us  from 
space  except  what  is  radiated  from  the  stars. 

Since,  then,  the  solar  heat  does  not  now  return  to  the  sun, 
we  have  to  inquire  what  becomes  of  it,  and  whether  a  com- 
pensation may  not  at  some  time  be  effected  wliereby  all  the 
lost  heat  will  be  received  back  again.  Now,  if  we  trace  the 
radiated  heat  into  the  wilds  of  space,  we  may  make  three  pos- 
sible liypotheses  respecting  its  ultimate  destiny  : 

1.  "We  may  suppose  it  to  be  absolutely  annihilated,  just  as  it 
was  formerly  supposed  to  be  annihilated  when  it  was  lost  by 
friction. 

2.  It  may  continue  its  onward  couree  through  space  forever. 

3.  It  may,  through  some  agency  of  which  we  have  no  con- 
ception, be  ultimately  gathered  and  returned  to  the  sources 
from  which  it  emanated. 

The  first  of  these  hypotheses  is  one  which  the  scientific 
thinkers  of  the  present  day  would  not  regard  as  at  all  philo- 
sophical. In  our  scientific  philosophy,  the  doctrine  that  force 
cannot  be  aimihilated  is  coequal  with  that  that  it  cannot  be 
created ;  and  the  inductive  processes  on  which  the  latter  doc- 
trine is  founded  are  almost  as  unimpeachable  as  those  from 
whicii  we  conclude  that  matter  cannot  be  created.  At  the 
same  time,  it  might  be  maintained  that  all  these  doctrines  re- 
specting the  uncreatableness  and  indestructibility  of  matter 
and  force  can  have  no  proper  foundation  except  induction 
from  experiment,  and  that  the  absolute  truth  of  a  doctrine 
like  this  cannot  be  proved  by  induction.  Especially  may  this 
be  claimed  in  respect  of  force.  The  most  careful  measures  of 
force  which  we  can  make  under  all  circumstances  show  that  it 


PEOGEESSIVE  CHANGES  IN  OUR  SYSTEM.  515 

Is  subject  to  no  sensible  loss  by  either  transmission  or  transfor- 
mation. But  this  alone  does  not  prove  that  it  can  be  subject 
to  no  loss  in  a  passage  through  space  requiring  hundreds  of 
thousands  or  millions  of  years.  There  is  also  this  essential 
difference  between  force  and  matter,  that  we  conceive  the  lat- 
ter as  made  up  of  individual  parts  which  preserve  their  iden- 
tity through  all  the  changes  of  form  which  they  undergo; 
while  force  is  something  in  which  we  do  not  conceive  of  any 
such  identity.  Thus,  when  I  allow  a  drop  of  water  to  evapo- 
rate from  my  hand,  I  can  in  imagination  trace  each  molecule 
of  water  through  the  air,  into  the  clouds,  and  down  to  the 
earth  again  in  some  particular  drop  of  rain,  so  that,  if  I  only 
had  the  means  of  actually  tracing  it,  I  could  say,  "  This  cup 
contains  one,  or  two,  or  twenty  of  the  identical  molecules 
which  evaporated  from  my  hand  a  week  or  a  month  ago." 
It  is  on  this  idea  of  the  separate  identity  of  each  molecule 
of  matter  that  our  opinion  of  the  indestructibility  of  matter  is 
founded,  because  matter  cannot  be  destroyed  without  destroy- 
ing individual  molecules,  and  any  cause  which  could  destroy  a 
single  molecule  might  equally  destroy  all  the  molecules  in  the 
universe. 

But  neither  parts  nor  identity  is  possible  in  force.  A  cer- 
tain amount  of  heat  may  be  expended  in  simply  raising  a 
weight.  Here  heat  has  disappeared,  and  is  replaced  by  a 
mere  change  of  position  —  something  which  cannot  be  con- 
ceived as  identical  with  it.  If  we  let  the  weight  drop,  the 
same  amount  of  heat  will  be  reproduced  that  was  expended 
in  raising  the  weight ;  but,  though  equal  in  quantity,  it  can- 
not be  regarded  as  identical  in  the  way  that  the  water  con- 
densed from  steam  is  identical  with  that  which  was  evapo- 
rated to  form  the  steam.  If  measures  showed  it  to  be  less 
in  quantity,  we  could  not  say  there  was  a  destruction  of  an 
identical  something  which  previousl}''  existed,  as  we  could  if 
the  condensed  steam  were  not  equal  to  the  water  evaporated. 
Therefore,  while  the  doctrine  of  the  indestructibility  of  force 
is  universally  received  as  a  scientific  principle,  it  can  hardly 
be  claimed  that  induction  has  established  its  absolute  correct- 


516  THE  STELLAR   UXIFEBSE. 

iiess;  and,  in  a  case  like  the  present,  where  we  see  something 
which  transcends  scientific  explanation,  the  failure  of  the 
widest  induction  may  be  considered  among  the  possible  alter- 
natives. 

The  second  alternative  —  that  the  heat  radiated  from  the 
sun  and  stare  continues  its  onward  course  through  space  for- 
ever— is  the  one  most  in  accord  with  our  scientific  concep- 
tions. We  actually  receive  heat  from  the  most  distant  star 
visible  in  our  telescopes,  and  this  heat  has,  according  to  the 
best  judgment  we  can  form,  been  travelling  thousands  of 
years  without  any  loss  whatever.  From  this  point  of  view, 
every  radiation  which  has  ever  emanated  from  the  earth  or 
the  sun  is  still  pursuing  its  course  through  the  stellar  spaces, 
without  any  other  diminution  than  that  which  arises  from  its 
being  spread  over  a  wider  area.  A  very  striking  presentation 
of  this  view  is,  we  believe,  due  to  some  modern  writer.  If 
an  intelligent  being  had  an  eye  so  keen  that  he  could  see  the 
smallest  object  by  the  faintest  light,  and  a  movement  so  rapid 
that  he  could  pass  from  one  bound  of  the  stellar  system  to  the 
other  in  a  few  years,  then,  by  viewing  the  earth  from  a  dis- 
tance much  less  than  that  of  the  farthest  star,  he  would  see  it 
by  light  which  had  left  it  several  thousand  years  before.  By 
simply  watching,  he  would  see  the  whole  drama  of  human  his- 
tory acted  over  again,  except  where  the  actions  had  been  hid 
den  by  clouds,  or  other  obstacles  to  the  free  radiation  of  light. 
The  light  from  every  human  action  performed  under  a  clear 
sky  is  still  pursuing  its  course  among  the  stars,  and  it  needs 
onlv  the  powei-s  we  have  mentioned  to  place  a  being  in  front 
of  the  ray,  and  let  him  see  the  action  again. 

If  the  hypothesis  now  under  consideration  be  the  correct 
one,  then  the  heat  radiated  by  the  sun  and  stars  is  forever  lost 
to  them.  There  is  no  known  way  by  which  the  heat  thus  sent 
off  can  be  returned  to  the  sun.  It  is  all  expended  in  produc- 
ing vibrations  in  the  ethereal  medium  which  constantly  ex- 
tend out  farther  and  farther  into  space. 

The  third  hypothesis,  like  the  first,  is  a  simple  conjecture 
permitted  by  the  necessary  imperfection  of  our  knowledge. 


THE  SOURCES  OF  THE  SUN'S  HEAT.  517 

All  the  laws  of  radiation  and  all  our  conceptions  of  space 
lead  to  the  conclusion  that  the  radiant  heat  of  the  sun  can 
never  be  returned  to  it.  Such  a  return  can  result  only  from 
space  itself  having  such  a  curvature  that  what  seems  to  us  a 
straight  line  shall  return  into  itself,  as  has  been  imagined  by  a 
great  Gerinan  nuthematician  ;*  or  from  the  ethereal  medium, 
the  vibrations  in  ^vhich  constitute  heat  being  limited  in  extent; 
or,  finall}',  thi'ougli  some  agency  as  yet  totally  unknown  to  sci- 
ence. The  first  idea  is  too  purely  speculative  to  admit  of  dis- 
cussion, while  the  other  two  suppositions  transcend  our  science 
as  completely  as  does  that  of  an  actual  annihilation  of  force. 

§  3.  The  Sources  of  the  Su7i^s  Heat. 

We  may  regard  it  as  good  as  an  observed  fact  that  the  sun 
has  been  radiating  heat  into  void  space  for  thousands  or  even 
millions  of  years,  without  any  apparent  diminution  of  the  sup- 
ply. One  of  the  most  difficult  questions  of  cosmical  physics — 
a  question  the  difficulty  of  which  was  not  seen  before  the  dis- 
covery of  the  conservation  of  force — has  been.  How  is  this  sup- 

*  This  idea  belongs  to  that  transcendental  branch  of  geometry  which,  rising 
above  those  conceptions  of  space  derived  from  our  experience,  investigates  wliat 
may  be  possible  in  the  relations  of  parts  of  space  considered  in  their  widest  range. 
It  is  now  conceded  that  the  supposed  a  priori  necessity  of  the  axioms  of  geom- 
etry has  no  really  sound  logical  foundation,  and  that  the  question  of  the  limita- 
tions within  which  they  are  true  is  one  to  be  settled  by  experience.  Especially  is 
this  true  of  the  tiieorem  of  parallels,  no  really  valid  demonstration  either  that  two 
parallel  straight  lines  will  never  meet  or  never  diverge  being  possible.  By  reject- 
ing the  limitations  imposed  upon  our  fundamental  geometrical  conceptions,  yet 
without  admitting  anything  wliich  positively  contradicts  them,  several  geometrical 
systems  have  been  constructed  in  recent  times,  which  are  included  under  tlie  gen- 
eral appellation  of  the  non-Euclidian  Geometry.  The  most  celel)rated  and  re- 
markable of  these  systems  is  tiiat  of  Riemaim,  who  showed  that  although  we  are 
obliged  to  conceive  of  space  as  unbounded,  since  no  position  is  possible  which  has 
not  space  on  all  sides  of  it,  yet  there  is  no  necessity  that  we  shall  consider  it  as 
infinite.  It  may  return  into  itself  in  something  the  manner  of  the  surface  of  a 
sphere,  which,  though  it  has  no  boundary,  yet  contains  only  a  finite  number  of 
square  feet,  and  on  which  one  who  travels  straight  forward  indefinitely  will  finally 
arrive  at  his  starting-point.  Although  this  idea  of  the  finitude  of  space  transcends 
our  fundamental  conceptions,  it  does  not  contradict  them,  and  the  most  that  ex- 
perience can  tell  us  in  the  matter  is  that,  though  space  be  finite,  the  whole  extent 
of  the  visible  universe  can  be  but  a  very  small  fraction  of  the  sum  total  of  space. 


518  THE  STELLAR    UXIVERSE. 

ply  of  heat  kept  up  ?  If  we  calculate  at  what  rate  the  tem- 
perature of  the  sun  would  be  lowered  annually  by  the  radia- 
tion from  its  surface,  we  shall  find  it  to  be  2|-°  Fahrenheit  per 
aimum,  supposing  its  specific  heat  to  be  the  same  as  that  of 
water,  and  from  5°  to  10°  per  annum,  if  we  suppose  it  the 
same  as  most  of  the  substances  which  compose  our  globe.  It 
would,  therefore,  have  entirely  cooled  off  in  a  few  thousand 
years  after  its  formation  if  it  had  no  other  source  of  heat 
than  that  shown  by  its  temperature. 

That  the  temperature  could  be  kept  up  by  combustion,  as 
terrestrial  fires  are  kept  up,  is  out  of  the  question,  as  new  fuel 
would  have  to  be  constantly  added  in  quantities  which  cannot 
possibly  exist  in  the  neighborhood  of  the  sun.  But  an  allied 
source  of  heat  has  been  suggested,  founded  on  the  law  of  the 
mechanical  equivalency  of  heat  and  force.  If  a  body  should 
fall  into  the  sun  from  a  great  height,  all  the  force  of  its  fall 
would  be  turned  into  heat,  and  the  heat  thus  produced  would 
be  enormously  greater  than  any  that  would  arise  from  the 
combustion  of  the  falling  body.  An  instance  of  this  law  is 
shown  by  the  passage  of  shooting-stai-s  and  aerolites  through 
our  atmosphere,  where,  though  the  velocity  rarely  amounts  to 
more  than  forty  miles  a  second,  nearly  all  such  bodies  are  con- 
sumed by  the  heat  generated.  Now,  the  least  velocity  with 
which  a  body  could  strike  the  sun  (unless  it  had  been  merely 
thrown  from  the  sun  and  had  fallen  back)  is  about  280  miles 
per  second ;  and  if  the  body  fell  from  a  great  height,  the  ve- 
locity would  be  over  350  miles  per  second.  The  meteoric 
theory  was  founded  on  this  law,  and  is,  in  substance,  that  the 
heat  of  the  sun  is  kept  up  by  the  impact  of  meteoi-s  upon  his 
surface.  The  fact  that  the  earth  in  its  course  around  the  sun 
encounters  millions  of  meteoroids  every  day  is  shown  by  the 
frequency  of  shooting -stars,  and  leads  to  the  result  that  the 
solar  system  is,  so  to  speak,  crowded  with  such  bodies  revolv- 
ing in  all  sorts  of  erratic  orbits.  It  is  therefore  to  be  sup- 
posed that  great  numbers  of  them  fall  into  the  sun ;  and  the 
question  whether  the  heat  thus  produced  can  be  equal  to  that 
radiated  by  the  sun  is  one  to  be  settled  by  calculation.     It  is 


THE  SOURCES  OF  THE  SUN'S  HEAT.  519 

thus  found  that,  in  order  to  keep  up  the  solar  heat,  a  mass  of 
matter  equal  to  our  planet  would  have  to  fall  into  the  sun  ev- 
ery century. 

This  quantity  of  meteoric  matter  is  so  far  beyond  all  rea- 
sonable possibility  that  it  requires  little  consideration  to  show 
that  the  supply  of  solar  heat  cannot  be  thus  accounted  for. 
Only  a  minute  fraction  of  all  the  meteoroids  or  other  bodies 
circulating  through  space  or  revolving  around  the  sun  could 
strike  that  luminary.  In  order  to  reach  the  sun,  they  would 
have  to  drop  directly  to  it  from  space,  or  be  thrown  into  it 
through  some  disturbance  of  their  orbits  produced  by  planet- 
ary attraction.  If  meteors  were  as  thick  as  this,  the  earth 
would  be  so  pelted  with  them  that  its  whole  surface  would  be 
made  hot  by  the  force  of  the  impact,  and  all  life  would  be 
completely  destroyed.  While,  then,  the  sun  may,  at  some  past 
time,  have  received  a  large  supply  of  heat  in  this  way,  it  is 
impossible  that  the  supply  could  always  be  kept  up. 

The  Contraction  Theory.  — It  is  now  known  that  there  is 
really  no  necessity  for  supposing  the  sun  to  receive  heat  from 
any  outward  source  whatever  in  order  to  account  for  the 
preservation  of  his  temperature  through  millions  of  years. 
As  his  globe  cools  oft"  it  must  contract,  and  the  heat  gener- 
ated by  this  contraction  will  suffice  to  make  up  almost  the  en- 
tire loss.  This  theory  is  not  only  in  accordance  with  the  laws 
of  matter,  but  it  admits  of  accurate  mathematical  investiga- 
tion. Knowing  the  annual  amount  of  energy  which  the  sun 
radiates  in  the  form  of  heat,  it  is  easy,  from  the  mechanical 
equivalent  of  the  heat  thus  radiated,  to  find  by  what  amount 
he  must  contract  to  make  it  up.  It  is  thus  found  that,  with 
the  present  magnitude  of  the  sun,  his  whole  diameter  need 
contract  but  220  feet  a  year  to  produce  all  the  heat  which  he 
radiates.  This  amounts,  in  round  numbers,  to  a  mile  in  25 
years,  or  four  miles  in  a  century. 

The  question  whether  the  temperature  of  the  sun  will  be 
raised  or  lowered  by  contraction  depends  on  whether  we  sup- 
pose his  interior  to  be  gaseous,  on  the  one  hand,  or  solid  or 
liquid,  on  the  other.    A  known  principle  of  the  contraction  of 


520  THE  STELLAR   UNIVERSE. 

gaseous  bodies,  and  one  which,  at  first  sight,  seems  paradox- 
ical, is  that  the  more  heat  such  a  body  loses,  the  hotter  it  will 
become.  By  losing  heat  it  contracts,  but  the  heat  generated 
by  the  contraction  exceeds  that  which  it  had  to  lose  in  order 
to  produce  the  contraction.*  When  the  mass  of  gas  is  so  far 
contracted  that  it  begins  to  solidify  or  liquefy,  this  action 
ceases  to  hold,  and  further  contraction  is  a  cooling  process. 
We  cannot  yet  say  whether  the  sun  has  or  has  not  begun  to 
solidify  or  liquefy  in  his  interior,  and  therefore  cannot  make 
an  exact  estimate  of  the  time  his  heat  will  last.  A  rough 
estimate  may,  however,  be  made  from  the  rate  of  contraction 
necessary  to  keep  up  the  present  supply  of  heat.  This  rate 
diminishes  as  the  sun  grows  smaller  at  such  a  rate  that  in  five 
millions  of  years  the  sun  will  be  reduced  to  one-half  his  pres- 
ent volume.  If  he  has  not  begun  to  solidify  now,  it  seems 
likely  that  he  will  then,  and  his  heat  must  soon  after  begin 
to  diminish.  On  the  whole,  it  is  quite  improbable  that  the 
sun  can  continue  the  radiation  of  sufficient  heat  to  support 
life  on  the  earth  ten  millions  of  years  more. 

The  contraction  theory  enables  us  to  trace  the  past  history 
of  the  sun  a  little  more  definitely  than  that  of  his  future.  He 
must  have  been  larger  a  hundred  years  ago  than  he  is  now  by 
four  miles,  and  yet  larger  in  preceding  centuries.     Knowing 


*  This  curious  law  of  cooling  masses  of  gas  was  discovered  by  Mr.  J.  Homer 
Lane,  of  Washington.  This  gentleman's  paper  on  the  theoretical  temperature  of 
the  sun,  in  tiie  American  Journal  of  Science  for  July,  1870,  contains  the  most 
profound  discussion  of  the  subject  with  which  I  am  acquainted.  The  principle  in 
question  may  be  readily  shown  in  the  following  way.  If  a  globular  gaseous  mass 
is  condensed  to  one-half  its  primitive  diameter,  the  central  attraction  upon  any 
part  of  its  mass  will  be  increased  fourfold,  while  the  surface  upon  which  this  at- 
traction is  exercised  will  be  reduced  to  one-fouvth.  Hence,  the  pressure  per  unit 
of  surface  will  be  increased  sixteen  times,  while  the  density  will  be  increased  only 
eight  times.  Hence,  if  the  elastic  and  gravitating  forces  were  in  equilibrium  in 
the  primitive  condition  of  the  gaseous  mass,  its  temperature  must  be  doubled  in 
order  that  they  may  still  be  in  equilibrium  when  the  diameter  is  reduced  one-half. 
A  similar  paradox  is  found  in  the  theorem  of  celestial  mechanics — that  the  effect 
of  a  resisting  medium  is  to  accelerate  tiie  motion  of  a  planet  or  comet  through 
it.  Tiie  effect  of  the  resistance  is  to  make  the  body  approach  the  sun,  and  the 
velocity  generated  by  the  approach  exceeds  that  lost  by  the  resistance. 


THE  SOURCES  OF  THE  SUN'S  HEAT.  521 

the  law  of  his  contraction,  we  can  determine  his  diameter  at 
any  past  time,  just  as  iu  the  case  of  the  running  clock  the 
height  of  the  weight  during  preceding  days  can  be  calculated. 
We  can  thus  go  back  to  a  time  when  the  globe  of  the  sun  ex- 
tended out  to  the  orbit  of  Mercury,  then  to  the  orbit  of  the 
earth,  and,  finally,  when  it  filled  the  whole  space  now  occupied 
by  the  solar  system.  "We  are  thus  led  by  a  backward  process 
to  the  doctrine  of  the  nebular  hypothesis  in  a  form  strikingly 
similar  to  that  in  which  it  was  presented  by  Kant  and  La- 
place, although  our  reasoning  is  founded  on  natural  laws  of 
which  those  great  thinkers  had  no  knowledge. 

If  we  take  the  doctrine  of  the  sun's  contraction  as  furnish- 
ing the  complete  explanation  of  the  solar  heat  during  the  whole 
period  of  the  sun's  existence,  we  can  readily  compute  the  total 
amount  of  heat  which  can  be  generated  by  his  contraction 
from  any  assigned  volume.  This  amount  has  a  limit,  liowever 
great  we  may  suppose  the  sun  to  have  been  in  the  beginning: 
a  body  falling  from  an  infinite  distance  would  generate  only 
a  limited  quantity  of  heat,  just  as  it  would  acquire  only  a  lim- 
ited velocity.  It  is  thus  found  that  if  the  sun  had,  in  the  be- 
ginning, filled  all  space,  the  amount  of  heat  generated  by  his 
contraction  to  his  present  volume  would  have  been  sufficient 
to  last  18,000,000  years  at  his  present  rate  of  radiation.  We 
can  say  with  entire  certainty  that  the  sun  cannot  have  been 
radiating  heat  at  the  present  rate  for  more  than  this  period  un- 
less he  has,  in  the  mean  time,  received  a  miraculous  accession 
of  energy  from  some  outside  source.  We  use  the  term  "  mi- 
raculous" to  designate  any  seeming  incompatibility  with  those 
well -ascertained  natural  laws  which  we  see  in  operation 
around  us.  These  laws  teach  us  that  no  body  can  acquire 
heat  except  by  changes  in  its  own  mass  akin  to  contraction  of 
its  parts,  or  by  receiving  it  from  some  other  body  hotter  than 
itself.  The  heat  evolved  by  contraction  from  an  infinite  size, 
or  by  the  falling  of  all  the  parts  of  the  sun  from  an  infinite 
distance,  shows  the  extreme  limit  of  the  heat  tlie  sun  could 
acquire  from  internal  change,  and  this  quantity,  as  just  stated, 
would  last  only   18,000,000  years.      In   order  that  the  sun 


522  THE  STELLAR    UXIVEESE. 

should  receive  lieat  from  another  body,  it  is  not  merely  neces- 
sary that  that  body  should  be  hotter  than  the  sun,  but  it  would 
have  to  be  so  much  hotter  that  the  small  fraction  of  its  radi- 
ant heat  which  reached  the  sun  would  be  greater  than  all  that 
the  sun  himself  radiated.  To  give  an  instance  of  what  this 
condition  requires,  we  remark  that  the  body  must  radiate 
more  heat  than  the  sun  in  the  proportion  that  the  entire  vis- 
ible celestial  sphere  bears  to  the  apparent  angular  magnitude 
of  the  body  as  seen  from  the  sun.  For  instance,  if  its  appar- 
ent diameter  were  twelve  degrees,  it  would  seem  to  till  about 
•g-gVrr  P^rt  of  the  celestial  sphere,  and  in  order  to  warm  the 
sun  at  all  it  would  have  to  radiate  more  than  three  thousand 
times  as  much  heat  as  the  sun  did.  Moreover,  in  order  to  fur- 
nish sufficient  heat  to  last  the  sun  any  given  length  of  time, 
it  would  have  to  stay  in  the  sun's  neighborhood  so  long  that 
the  excess  of  what  the  sun  received  over  what  he  radiated 
would  furnish  a  supply  of  heat  sufficient  for  that  time.  We 
cannot  suppose  the  sun  to  have  received  even  a  supply  of  a 
thousand  yeai-s  of  heat  in  this  way  without  the  most  extrava- 
gant assumptions  respecting  the  volume,  the  temperature,  and 
the  motion  of  the  body  from  which  the  heat  was  recei\ed — 
assumptions  which,  in  addition  to  their  extravagance,  would 
involve  the  complete  destruction  of  the  planets  by  the  heat  of 
the  body,  and  the  total  disarrangement  of  their  orbits  by  its 
attraction,  if  we  suppose  them  to  have  been  in  any  way  pro- 
tected from  this  heat. 

The  foregoing  computation  of  the  limit  of  time  the  sun  can 
have  been  radiating  heat  is  founded  on  the  supposition  that 
the  amount  of  heat  radiated  has  always  been  the  same.  If 
we  suppose  this  amount  to  have  been  less  formei'ly  than  now, 
the  period  of  the  sun's  existence  may  have  been  longer,  and 
in  the  contrary  case  it  may  have  been  shorter.  The  amount 
in  question  depends  on  several  causes,  the  effect  of  which  can- 
not be  accurately  computed — namely,  the  magnitude,  temper- 
ature, and  condition  of  the  solar  globe.  Supposing  a  uniform 
radiation,  the  diameter  of  this  globe  was  twice  as  great  nine 
millions  of  yeai*s  ago  as  it  is  now.     Its  surface  was  then  of 


SECULAR   COOLING   OF  THE  EARTH.  523 

four  times  its  present  extent,  so  that,  if  it  was  of  the  same 
nature  and  at  the  same  temperature  as  now,  there  would  have 
been  four  times  the  radiation.  But  its  density  would  have 
been  only  one-eighth  as  great  as  at  present,  and  its  temper- 
ature would  have  been  lower.  These  circumstances  would 
tend  to  diminish  its  radiation,  so  that  it  is  quite  possible  that 
the  total  amount  of  heat  radiated  was  no  greater  than  at 
present.  The  probability  would  seem  to  be  on  the  side  of  a 
greater  total  radiation,  and  this  probability  is  strengthened  by 
geological  evidence  that  the  earth  was  warmer  in  its  earlier 
ages  than  now.  If  we  reflect  that  a  diminution  of  the  solar 
heat  by  less  than  one-fourth  its  amount  would  probably  make 
our  earth  so  cold  that  all  the  water  on  its  surface  would 
freeze,  while  an  increase  by  much  more  than  one-half  would 
probably  boil  the  water  all  away,  it  must  be  admitted  that  the 
balance  of  causes  which  would  result  in  the  sun  radiating  heat 
just  fast  enough  to  preserve  the  earth  in  its  present  state  has 
probably  not  existed  more  than  10,000,000  years.  This  is, 
therefore,  near  the  extreme  limit  of  time  that  we  can  suppose 
water  to  have  existed  on  the  earth  in  the  fluid  state. 

§  4.  Secular  Cooling  of  the  Earth. 

An  instance  of  a  progressive  loss  of  heat,  second  in  impor- 
tance only  to  the  loss  from  the  sun  itself,  and,  indeed,  con- 
nected with  it,  is  afforded  by  the  secular  cooling  of  the  earth. 
As  we  have  shown  in  a  preceding  chapter,  the  interior  of  the 
earth  is  hotter  than  the  surface,  and  wherever  there  is  such 
a  difference  of  temperature  as  this,  there  must  be  a  conduc- 
tion of  heat  from  the  hotter  to  the  colder  parts.  In  order 
that  heat  may  thus  be  conducted,  there  must  be  a  supply  of 
heat  inside.  The  increase  of  heat  downwards  into  the  earth 
cannot,  therefore,  terminate  suddenly,  but  must  extend  to  a 
great  depth. 

Whatever  view  we  may  take  of  the  question  of  the  earth's 
fluidity,  it  must  be  admitted  that  it  was  hotter  in  former  ages 
than  now.  To  borrow  an  illustration  from  Sir  William  Thom- 
son, the  case  is  much  the  same  as  if  we  should  find  a  hot  stone 


524  THE  STELLAR   UNIVERSE. 

in  a  field.  We  could  say,  with  entire  certainty,  that  the  stone 
had  been  in  the  fire,  or  some  other  hot  place,  within  a  limited 
period  of  time.  Respecting  the  origin  of  this  heat,  two  hy- 
potheses have  prevailed — one,  founded  on  the  nebular  theory, 
that  the  earth  was  originally  condensed  as  a  molten  mass,  and 
has  not  yet  cooled  off ;  the  other,  that  it  received  its  heat  from 
some  external  source.  The  latter  was  the  view  of  Poisson, 
who  accounted  for  the  increase  of  temperature  by  supposing 
that  the  solar  system  had,  at  some  former  period,  passed 
through  a  hotter  region  of  space  than  that  in  which  it  is  now 
found.  This  view  is,  however,  now  known  to  be  entirely  un- 
tenable, for  several  reasons.  Space  itself  cannot  be  warm, 
and  the  earth  could  have  derived  heat  only  from  passing  near 
a  hot  body.  A  star  passing  near  enough  to  heat  up  the  earth 
would  have  totally  disarranged  the  planetary  orbits,  by  its  at- 
traction, and  destroyed  all  life  on  the  surface  of  the  globe  by 
its  heat. 

Thus,  tracing  back  the  earth's  heat,  we  are  led  back  to  the 
time  when  it  was  white-hot ;  and  then,  again,  to  when  it  was 
enveloped  in  the  fiery  atmosphere  of  the  sun  ;  and  again,  when 
it  was  itself  a  mass  of  fiery  vapor.  Respecting  the  time  re- 
quired for  it  to  cool  off,  we  cannot  make  any  exact  calcula- 
tion, as  we  have  done  in  the  case  of  the  sun,  because  the  cir- 
cumstances are  entirely  different.  Owing  to  the  solidity  of  at 
least  the  outer  crust  of  the  earth,  the  heat  which  it  loses  bears 
no  known  relation  to  its  interior  temperature.  In  fact,  were 
we  to  compute  how  long  the  earth  might  liave  been  able  to 
radiate  heat  at  its  present  rate,  we  may  find  it  to  be  counted 
by  hundreds  or  thousands  of  millions  of  years.  The  kernel 
of  the  difficulty  lies  in  the  fact  that  whei^  a  solid  crust  once 
formed  over  the  molten  earth,  there  was  a  sudden  change  in 
the  rate  of  cooling.  As  long  as  the  globe  was  molten,  there 
would  be  constant  currents  between  its  surface  and  the  inte- 
rior, the  cooling  superficial  portion  constantly  sinking  down, 
and  being  replaced  by  fresh  hot  matter  from  the  interior. 
But  when  a  continuous  solid  crust  was  once  formed,  the  heat 
could  reach  the  sui-face  only  by  conduction  through  the  crust, 


SECULAR  COOLING  OF  THE  EARTH.  525 

and  the  latter,  though  only  a  few  feet  thick,  would  operate  as 
a  screen  to  prevent  tlie  further  loss  of  heat.  There  would,  as 
the  crust  cooled,  be  enormous  eruptions  of  molten  matter  from 
the  interior;  but  these  w^ould  rapidly  cool,  and  thus  help  to 
thicken  the  crust. 

A  fact  not  to  be  lost  sight  of,  and  which  in  some  way  as- 
similates the  earth  to  the  sun,  is  that  of  the  heat  lost  by  the 
earth  by  far  the  greater  part  is  made  up,  not  by  a  lowering 
of  the  temperature  of  the  earth,  but  by  its  contraction.  It  is 
true  that  there  must  be  some  lowering  of  temperature,  but  for 
each  degree  that  the  temperature  is  lowered  there  will  proba- 
bly be  a  hundred  degrees  of  heat  evolved  by  the  contraction 
of  our  globe.  Considering  only  the  earth,  it  is  difficult  to  set 
an  exact  limit  to  the  time  it  may  have  been  cooling  since  its 
crust  was  formed. 

The  sudden  change  produced  in  the  radiation  of  a  molten 
body  by  the  formation  of  a  solid  crust  over  its  surface  may 
afford  us  some  clue  to  the  probable  termination  of  the  heat- 
giving  powers  of  the  sun.  Whenever  the  latter  so  far  cools 
off  that  a  continuous  solid  crust  is  formed  over  its  surface,  it 
will  rapidly  cease  to  radiate  the  heat  necessary  to  support  life 
on  the  globe.  At  its  present  rate  of  radiation,  the  sun  will  be 
as  dense  as  the  eartli  in  about  12,000,000  years ;  and  it  is 
quite  likely  to  be  long  before  that  time  that  we  are  to  expect 
the  permanent  formation  of  such  a  crust. 

The  general  cosmical  theory  which  we  have  been  consider- 
ing accounts  for  the  supposed  physical  constitution  of  Jupiter, 
which  has  been  described  in  treating  of  that  planet.  On  the 
nebular  hypothesis,  as  we  have  set  it  forth,  tlie  ages  of  the 
several  planets  do  not  greatly  differ.  The  smaller  planets 
would,  therefore,  cool  off  sooner  than  the  larger  ones.  It  is 
possible  that,  owing  to  the  great  masses  of  Jupiter  and  Saturn, 
their  rate  of  cooling  has  been  so  slow  that  no  solid  crust  is  yet 
formed  over  them.  In  this  case  they  would  appear  self-lumi- 
nous, M^ere  they  not  surrounded  by  immense  atmospheres,  filled 
with  clouds  and  vapors,  which  shut  off  a  great  part  of  the 
internal  heat,  and  thus  delay  the  cooling  process. 


526  TEE  STELLAR   UNIVERSE. 

§  5.  General  Conclusions  respecting  the  Nebula)-  Hrjpoihesis. 
It  would  seem  from  what  has  been  said  that  the  widest  in- 
ductions of  modern  science  agree  with  the  speculations  of 
thinking  minds  in  past  ages,  in  presenting  the  creation  of  the 
material  nnivei-?e  to  our  view  as  a  process  ratlier  than  an  act. 
This  process  began  when  the  present  material  nnivei-se  was  a 
mass  of  fiery  vapor,  filling  the  stellar  spaces ;  it  is  still  going 
on  in  its  inevitable  course,  and  it  will  end  when  sun  and  stars 
are  reduced  to  dark  and  cold  masses  of  dead  matter.  The 
thinking  reader  will,  at  this  stage  of  the  inquiry,  very  natu- 
rally inquire  whether  this  view  of  the  cosmogony  is  to  be 
received  as  an  established  scientific  fact,  or  only  as  a  result 
which  science  makes  more  or  less  probable,  but  of  the  validity 
of  which  opinions  may  reasonably  differ.  We  consider  that 
the  latter  is  the  more  correct  view.  All  scientific  conclusions 
necessarily  rest  on  the  postulate  that  the  laws  of  nature  are 
absolutely  unchangeable,  and  that  their  operations  have  never 
been  interfered  with  by  the  action  of  any  supernatural  cause ; 
that  is,  by  any  cause  not  now  in  operation  in  nature,  or  op- 
erating in  any  way  different  from  that  in  which  it  has  always 
done.  The  question  of  the  correctness  of  this  postulate  is  one 
of  philosophy  and  common-sense  rather  than  of  science ;  and 
all  we  can  say  in  its  favor  is  that,  as  a  general  rule,  the  bet- 
ter men  understand  it,  the  more  difliculty  they  find  in  doubting 
it.  And  all  we  can  say  in  favor  of  the  nebular  hypothesis 
amounts  to  this :  that  the  operations  of  nature,  in  their  widest 
range,  when  we  trace  them  back,  seem  to  lead  us  to  it,  as 
the  mode  of  running  of  the  clock  leads  to  the  conclusion  that 
it  was  once  wound  up. 

Helmholtz,  Thomson,  and  others  have,  as  we  have  explain- 
ed, made  it  evident  that  by  tracing  back  the  cooling  processes 
we  now  see  going  forward  in  nature,  we  are  led  to  a  time 
when  the  planets  were  enveloped  in  the  fiery  atmosphere  of 
the  sun,  and  were  therefore  themselves  in  a  molten  or  vapor- 
ous form.  But  the  reverse  problem,  to  show  that  a  nebulous 
mass  would  or  might  condense  into  a  system  possessing  the 


CONCLUSIONS  RESPECTING  THE  NEBULAR  HYPOTHESIS.    527 

wonderful  symmetry  of  our  solar  system — the  planets  revolv- 
ing round  the  sun,  and  the  satellites  round  their  primaries 
in  nearly  circular  orbits — has  not  been  solved  in  a  manner  at 
all  satisfactory.  AVe  have  seen  that  Kant's  ideas  were  in  some 
respects  at  variance  with  the  laws  of  mechanics  which  have 
since  been  discovered.  Laplace's  explanation  of  how  the 
planets  might  have  been  formed  from  the  atmosphere  of  the 
sun  is  not  mathematical  enough  to  be  conclusive.  In  the  ab- 
sence of  a  mathematical  investigation  of  the  subject,  it  seems 
more  likely  that  the  solar  atmosphere  would,  under  the  condi- 
tions supposed  by  Laplace,  condense  into  a  swarm  of  small 
bodies  like  the  asteroids,  filling  the  whole  space  now  occupied 
by  the  planets.  Again,  when  we  examine  the  actual  nebulae, 
we  find  very  few  of  them  to  present  that  symmetry  of  outline 
which  would  lead  to  their  condensation  into  a  system  so  sym- 
metrical as  that  to  which  our  planet  belongs.  The  double 
stars,  revolving  in  orbits  of  every  degree  of  eccentricity,  and 
the  rings  of  Saturn,  composed  apparently  of  a  swarm  of  small 
particles,  offer  better  examples  of  what  we  should  expect  from 
the  nebular  hypothesis  than  do  the  planets  and  satellites  of  our 
system. 

These  difficulties  may  not  be  insurmountable.  The  greatest 
of  them,  perhaps,  is  to  show  how  a  ring  of  vapor  surrounding 
the  sun  could  condense  into  a  single  planet  encircled  by  satel- 
lites. The  conditions  under  which  such  a  result  is  possible 
require  to  be  investigated  mathematically.  At  the  present 
time  we  can  only  say  that  the  nebular  hypothesis  is  indicated 
by  the  general  tendencies  of  the  laws  of  nature ;  that  it  has 
not  been  proved  to  be  inconsistent  with  any  fact;  that  it  is 
almost  a  necessary  consequence  of  the  only  theory  by  which 
we  can  account  for  the  origin  and  conservation  of  the  sun's 
heat ;  but  that  it  rests  on  the  assumption  that  this  conservation 
is  to  be  explained  by  the  laws  of  nature,  as  we  now  see  them 
in  operation.  Should  any  one  be  sceptical  as  to  the  sufficiency 
of  these  laws  to  account  for  the  present  state  of  things,  science 
can  furnish  no  evidence  strong  enough  to  overthrow  his  doubts 
until  the  sun  shall  be  found  growing  smaller  by  actual  raeas- 

35 


528  THE  STELLAR   UNIVERSE. 

urement,  or  the  nebulae  be  actually  seen  to  condense  into  stare 
and  systems. 

§  6.  The  Plurality  of  Worlds. 

"When  vre  contemplate  the  planets  as  worlds  like  our  own, 
and  the  stars  as  suns,  each,  perhaps,  with  its  retinue  of  attend- 
ant planets,  the  idea  naturally  suggests  itself  that  other  planets 
as  well  as  this  may  be  the  abode  of  intelligent  beings.  The 
question  whether  other  planets  are,  as  a  general  rule,  thus 
peopled,  is  one  of  the  highest  interest  to  us,  not  only  as  in- 
volving our  place  in  creation,  but  as  showing  us  what  is  really 
greatest  in  the  universe.  Many  thinking  people  regard  the 
discovery  of  evidences  of  life  in  other  worlds  as  the  great  ul- 
timate object  of  telescope  research.  It  is,  therefore,  extreme- 
ly disappointing  to  learn  that  the  attainment  of  any  direct 
evidence  of  such  life  seems  entirely  hopeless — so  hopeless, 
indeed,  that  it  has  almost  ceased  to  occupy  the  attention  of 
astronomers.  The  spirit  of  modern  science  is  wholly  adverse 
to  speculation  on  questions  for  the  solution  of  which  no  scien- 
tific evidence  is  attainable,  and  the  common  answer  of  astron- 
omers to  all  questions  respecting  life  in  other  worlds  would 
be  that  they  knew  no  more  on  the  subject  than  any  one  else, 
and,  having  no  data  to  reason  from,  had  not  even  an  opinion 
to  express.  Still,  in  spite  of  this,  many  minds  will  speculate ; 
and  although  science  cannot  answer  the  great  question  for  us, 
she  may  yet  guide  and  limit  our  speculations.  It  may,  there- 
fore, not  be  unprofitable  to  show  within  Mliat  limits  specula- 
tion may  not  be  discordant  with  the  generalizations  of  science. 

First,  we  see  moving  round  our  sun  eight  large  planets,  on 
one  of  which  we  live.  Our  telescopes  show  us  other  suns,  in 
such  numbei-s  that  they  defy  count,  amounting  certainly  to 
many  millions.  Are  these  suns,  like  our  own,  centres  of  plan- 
etary systems?  If  our  telescopes  could  be  made  powerful 
enough  to  show  such  planets  at  distances  so  immense  as  those 
of  the  fixed  stars,  the  question  would  at  once  be  settled ;  but 
all  the  planets  of  our  system  would  disappear  entirely  from 
the  reach  of  the  most  powerful  telescopes  we  can  ever  hope  to 


TRE  PLURALITY  OF  WORLDS.  529 

make  at  a  distance  far  less  than  that  which  separates  us  from 
the  nearest  fixed  star.  Observation  can,  therefore,  afford  us 
no  information  on  the  subject.  We  must  have  recourse  to 
cosmological  considerations,  and  these  may  lead  to  the  con- 
clusion that  if  the  whole  universe  condensed  from  a  nebulous 
mass,  the  same  cause  which  led  our  sun  to  be  surrounded  bj 
planets  would  operate  in  the  case  of  other  suns.  But  we  have 
just  shown  that  the  symmetry  of  form  and  arrangement  seen 
in  our  system  is  something  we  could  rarely  expect  to  result 
from  the  condensation  of  masses  so  irregular  as  those  which 
make  up  the  large  majority  of  the  nebulse,  while  the  irreg- 
ular orbits  of  the  double  stars  show  us  what  we  should  rather 
expect  to  be  the  rule.  It  is,  therefore,  quite  possible  that  reti- 
nues of  planets  revolving  in  circular  orbits  may  be  rare  excep- 
tions,  rather  than  the  rule,  among  the  stars. 

Next,  granting  the  existence  of  planets  without  number, 
what  indications  can  we  have  of  their  habitability  ?  There 
is  one  planet  besides  our  own  for  which  the  telescope  settles 
this  point — namely,  the  moon.  This  body  has  neither  air  nor 
water,  and,  consequently,  nothing  on  which  organic  life  can 
be  supported.  The  speculations  sometimes  indulged  in  re- 
specting the  possible  habitability  of  the  other  side  of  the 
moon,  which  we  can  never  see,  are  nothing  more  than  plays 
of  the  imagination.  The  primary  planets  are  all  too  distant 
to  enable  us  to  form  any  certain  judgment  of  the  nature  of 
their  surfaces,  and  the  little  we  can  see  indicates  that  their 
constitution  is  extremely  varied.  Mars  has  every  appearance 
of  being  like  our  earth  in  many  particulars,  and  is,  therefore, 
the  planet  which  we  should  most  expect  to  find  inhabited. 
Most  of  the  other  planets  give  indications  of  being  surround- 
ed by  immense  atmospheres,  filled  with  clouds  and  vapors, 
through  which  sight  cannot  penetrate,  and  we  can  reach  no 
certain  knowledge  of  what  may  be  under  these  clouds.  On 
the  whole,  we  may  consider  the  chances  to  be  decidedly 
against  the  idea  that  any  considerable  fraction  of  the  heav- 
enly bodies  are  fitted  to  be  the  abode  of  such  animals  as  we 
have  on  the  earth,  and  that  the  number  of  them  which  have 


530  TEE  STELLAR  UNIVERSE. 

the  requisites  for  supporting  civilization  is  a  very  small  fraC' 
tion  indeed  of  the  whole. 

This  conclusion  rests  on  the  assumption  that  the  conditions 
of  life  are  the  same  in  other  worlds  as  in  our  own.  This  as- 
sumption may  be  contested,  on  the  ground  that  we  can  set  no 
limits  to  the  power  of  the  Creator  in  adapting  life  to  the  con- 
ditions which  surround  it,  and  that  the  immense  range  of  adap- 
tation on  our  globe — some  animals  living  where  others  are  im- 
mediately destroyed — makes  all  inferences  founded  on  the  im- 
possibility of  our  earthly  animals  living  in  the  planets  entirely 
inconclusive.  The  only  scientific  way  of  meeting  this  argu- 
ment is  to  see  whether,  on  our  earth,  there  are  any  limits  to 
the  adaptabiUty  in  question.  A  cursory  examination  shows 
that  while  there  are  no  well-defined  limits  to  what  may  be 
considered  as  life,  the  higher  forms  of  animal  life  are  very 
far  from  existing  equally  under  all  conditions,  and  the  high- 
er the  form,  the  more  restricted  the  conditions.  We  know 
that  no  animal  giving  evidence  of  self-consciousness  is  devel- 
oped except  under  the  joint  influence  of  air  and  water,  and 
between  certain  narrow  limits  of  temperature;  that  only  forms 
of  life  which  are  intellectually  very  low  are  developed  in  the 
ocean ;  that  there  is  no  adapting  power  exercised  by  nature  on 
our  globe  whereby  man  can  maintain  a  high  degree  of  intel- 
lectual or  bodily  vigor  in  the  polar  regions ;  that  the  heats  of 
the  torrid  zone  also  impose  restrictions  upon  the  development 
of  our  race.  The  conclusion  which  we  may  draw  from  this 
is  that,  if  great  changes  should  occur  on  the  surface  of  our 
globe,  if  it  should  be  cooled  down  to  the  temperature  of  the 
poles,  or  heated  up  to  that  of  the  equator,  or  gradually  be  cov- 
ered with  water,  or  deprived  of  its  atmosphere,  the  higher  pres^ 
ent  forms  of  animal  life  would  refuse  to  adapt  themselves  to 
the  new  state  of  things,  and  no  new  forms  of  life  of  equal  ele- 
vation would  take  the  place  of  those  destroyed  by  the  change. 
There  is  not  the  slightest  reason  for  believing  that  anything 
more  intelligent  than  a  fish  would  ever  live  under  water,  or 
anything  more  intellectual  than  the  Esquimaux  ever  be  sup- 
ported in  regions  as  cold  as  the  poles.     If  we  apply  this  con- 


THE  PLURALITY  OF  WORLDS.  531 

sideration  to  the  question  which  now  occupies  us,  we  are  led 
to  the  conclusion  that,  in  view  of  the  immense  diversity  of 
conditions  which  probably  prevails  in  the  universe,  it  would 
be  inly  in  a  few  favored  spots  that  we  should  expect  to  find 
any  very  interesting  development  of  life. 

An  allied  consideration  will  lead  us  to  nearly  the  same  con- 
clusion. Enthusiastic  writers  not  only  sometimes  people  the 
planets  with  inhabitants,  but  calculate  the  possible  population 
by  the  number  of  square  miles  of  surface,  and  throw  in  a  lib- 
eral supply  of  astronomers  who  scan  our  earth  with  powerful 
telescopes.  The  possibility  of  this  it  would  be  presumption 
to  deny ;  but  that  it  is  extremely  improbable,  at  least  in  the 
case  of  any  one  planet,  may  be  seen  by  reflecting  on  the  brev- 
ity of  civilization  on  our  globe,  when  compared  with  the  exist- 
ence of  the  globe  itself  as  a  planet.  The  latter  has  probably 
been  revolving  in  its  orbit  ten  millions  of  years ;  man  has 
probably  existed  on  it  less  than  ten  thousand  years;  civiliza- 
tion less  than  four  thousand ;  telescopes  little  more  than  two 
hundred.  Had  an  angel  visited  it  at  intervals  of  ten  thousand 
years  to  seek  for  thinking  beings,  he  would  have  been  disap- 
pointed a  thousand  times  or  more.  Reasoning  from  analogy, 
we  are  led  to  believe  that  the  same  disappointments  might 
await  him  who  should  now  travel  from  planet  to  planet,  and 
from  system  to  system,  on  a  similar  search,  until  he  had  exam- 
ined many  thousand  planets. 

It  seems,  therefore,  so  far  as  we  can  reason  from  analogy, 
that  the  probabilities  are  in  favor  of  only  a  very  small  frac- 
tion of  the  planets  being  peopled  with  intelligent  beings. 
But  when  we  reflect  that  the  possible  number  of  the  planets 
is  counted  by  hundreds  of  millions,  this  small  fraction  may 
be  really  a  very  large  number,  and  among  this  number  many 
may  be  peopled  by  beings  much  higher  than  ourselves  in  the 
intellectual  scale.  Here  we  may  give  free  rein  to  our  imagi- 
nation, with  the  moral  certainty  that  science  will  supply  noth- 
ing tending  either  to  prove  or  to  disprove  any  of  its  fancies. 


APPENDIX. 


I. 

LIST  OF  THE  PRINCIPAL  GREAT  TELESCOPES  OF  THE  Wt)RlD. 

A.  Reflecting  Telescopes. 


tr,  and  Place. 


The  Earl  of  Rosse,  Parsonstown, 
Ireland 

Mr.  A.  A.  Common,  Ealing,  Eng- 
land  

The  Observatory  of  Melbourne, 
Australia 

The  Observatory  of  Paris 


The  Earl  of  Rosse,  Parsonstown, 
Ireland 

Mrs.  Henry  Draper,  Dobb's  Fer- 
ry, New  York 

The  Observatory  of  Toulouse, 
France  

The  Observatory  of  Marseilles, 
France  


Construction.* 

Aperture. 

Newtonian. 

6  feet. 

Newt.,  S.G. 

37  in. 

Cassegr. 

4  feet. 

Newt.,  S.  G. 

47  in. 

Newtonian. 

3  feet. 

Cass.,  S.  G. 

28  in. 

S.G. 

31.5  in. 

S.G. 

31.5  in. 

Maker,  and  Date. 


Earl  of  R.,  1844. 

j  The  owner  and  Mr. 
]       Calver. 

Mr.  Grubb,  1870. 

j  M.  Martin  and  M. 

]      Eichens,  1875. 

The  owner. 
The  owner. 

M.  Foucault. 

j  M.  Foucault  and  M. 
{      Eichens. 


B.  Refracting  Telescopes. 


Owner,  and  Place. 


The  Lick  Observatory  of  California , 

The  Observatory  of  Nice,  France 

The  Imperial  Observatory,  Pulkowa,  Russia. 

The  Imperial  Observatory,  Vienna 

U.  S.  Naval  Observatory,  Washington 

The  University  of  Virginia 

Mr.  R.  S.  Newall,  Gateshead,  England 

The  Observatory  of  Strasburg,  Germany.  .  .  . 

The  Observatory  of  Chicago 

Mr.  Van  der  Zee,  Buffalo,  New  York 


The   Observatory  of  Harvard  College,  Cam-  ) 
bridge,  Mass [ 


Aperture. 


36 

in. 

30 

in. 

30 

in. 

27 

in. 

26 

in. 

26 

in. 

25 

in. 

19 

in. 

18.5  in 

18 

in. 

15 

in. 

Maker,  and  Date. 


j  A.  Clark  and  Sons, 

\       1887. 

The  Henrys,  1886. 

j  A.  Clark  and  Sons, 

\       1883. 

Mr.  Gruhb,  1881. 

j  A.  Clark  and  Sons, 

\      1873. 

j  A.  Clark  and  Sons, 

I   1881. 

j  T.  Cooke  and  Sons, 

I      1870. 

Merz  and  Miihler. 

\  A.  Clark  and  Sons, 

1       1862. 

Mr.  Fitz,  of  N.  Y. 

j  Merz  and  Mahler, 

\       1843. 


•  In  this  column  "  Cassegr."  signifles  the  Cassegraiuian  constmction,  described  on  page 
126.    S.  G.  siguifies  that  the  mirror  is  of  silvered  glass. 


534 


APPENDIX. 


Oirner,  and  Place. 


The  Rojal  Observatory,  Pulkowa,  Russia 

Mr.  William  Huggins,  London,  England* 

Lord  Lindsay,  Aberdeen,  Scotland 

The  Observatory  of  Lisbon,  Portugal 

The  Observatory,  Markree  Castle,  England 

Hamilton  College,  Clinton,  New  York 

The  Paris  Observatoryf 

The  Allegheny  Observatory,  Pennsylvania 

Mr.  L.  M.  Rutherfurd,  Xew"  York 

The  Dudley  Observatory,  Albany,  New  York. . . . 

The    Royal    Observatory,    Greenwich,    Eng-  ) 
land}; ) 

Michigan  University,  Ann  Arbor 

Vassar  College,  Poughkeepsie,  New  York 

The  Physical  Observatory,  Oxford,  England 

The  Imperial  Observatory,  Vienna 

The  Cambridge  Observatory,  England 

The  Royal  Observatory,  Dublin 

Professor  Henry  Draper,  Dobbs  Ferrv,  New  ) 
York '. ) 

The  Pritchett  Institute,  Glasgow,  Missouri 

Mr.  S.  V.  White,  Brooklyn,  New  York 

The  Radcliffe  Observatory,  Oxford,  England . . .  . 
The  Lick  Observatory,  San  Jose,  California.  . . 

The  Observatory,  Bothkamp,  Germany 

The  Observatory,  Cordova,  South  America 

The  Observatory,  Munich,  Germany , 

The  Observatory,  Copenhagen,  Denmark 

The  Observatory  of  Cincinnati,  Ohio 

Middletown  University,  Connecticut , 


Aperture. 


15  in. 

15  in. 
15  in. 
14.8  in. 
14  in. 
13.5  in. 
13  in. 
13  in. 
13  in. 
13  in. 


12.5  in. 

12.5  in. 

12.3  in. 

12.2  in. 

12  in. 

12  in. 
12  in. 

12  in. 

12  in. 

12  in. 
12  in. 
12  in. 
11.7  in. 
11.2  in. 
11  in. 
11  in. 
11  in. 
11  in. 


Maker,  and  Date. 


\ 


I  Merz  and  Mahler, 
\      1840. 
Mr.  Grubb. 
Mr.  Grubb. 
Merz  and  Mahler. 


Mr.  Spencer. 
M.  Eichens. 


The  owner. 
Mr.  Fitz,  of  N.  Y. 
f  Merz     and     Sons, 
1860. 
Troughton        and 
Simms. 
Mr.  Fitz,  of  N.  Y. 
\  Mr.  Fitz,  of  N.  Y. 
]  A.  Clark  and  Sons. 
Mr.  Grubb. 
j  A.  Clark  and  Sons, 
I       1876. 
M.  Cauchoix. 
M.  Cauchoix. 
^  A.  Clark  and  Sons, 
\      1876. 

]  A.  Clark  and  Sons, 
(      1876. 

A.  Clark  and  Sons. 
M.  Cauchoix. 
A.  Clark  and  Sons. 
Schroeder. 
Mr.  Fitz,  of  N.  Y. 
Merz. 
Merz. 
Merz. 
A.  Clark  and  Sons. 


Besides  these,  the  following  three  telescopes  are  projected :  a  28-iuch  re- 
fractor for  the  Greenwich  Observatory,  by  Grubb,  of  Dublin ;  a  great  re- 
fractor for  the  Paris  Observatory,  to  be  figured  by  the  brothers  Heury,  of 
Paris ;  a  refractor  of  28  inches  for  Yale  College,  by  A.  Clark  and  Sons. 

•  This  telescope  belongs  to  the  Royal  Society,  bnt  is  in  possession  of  Mr.  Haggius. 

t  The  object-glass  is  an  old  one,  but  the  mounting  is  new,  by  Eichens. 

X  The  object-glass  is  by  Mera,  of  Munich,  the  mounting  by  Troughton  and  Simma. 


LIST  OF  THE  MORE  REMARKABLE  DOUBLE  STARS.    535 


11. 

LIST  OF  THE  MORE  REMARKABLE  DOUBLE  STARS. 

COMPILED    BY    S.   VT.   BCRNHAM. 


Right  Ascen. 

DeclinatiOD 

Positi'n 

Name. 

1880. 

1880. 

Angle. 

Distance. 

Magnitudes. 

Notes, 

H.    M.     S. 

0       / 

. 

„ 

35  Piscium  . . . 

8  47 

8     9 

149.8 

11.53 

6.2 

7.8 

j  White, 2.  Pale-white: 
1     violet,  Smyth. 

38        "      ... 

11   13 

8  12 

237.6 

4.59 

7.0 

8.0 

42        "      ... 

16  13 

12  49 

338.0 

29.73 

6.8 

10.7 

j  Yellow  :  blue  -  green, 
1      Herschel. 

51         "      ... 

26  12 

6  18 

82.3 

27.42 

5.0 

9.0 

White :  ashy. 

55         "       ... 

33  36 

20  47 

192.7 

6.37 

5.0 

8.2 

j  Yellow  :     deep  -  red, 
I      Dembowski. 

J)  Cassiopeae. . . 

41  43 

57  11 

140.0 

5.86 

4.0 

7.6 

Yellow :  purple. 

SoAndromedae. 

48  32 

22  59 

358.9 

1.34 

6.2 

6.8 

Binary,  349.1  years. 

<p  Piscium  .... 

1     Y  14 

23  57 

227.5 

7.98 

4.7 

10.1 

White:  blue. 

42  Ceti 

13  41 

-1     8 

351.4 

1.25 

6.2 

7.2 

Polaris 

13  45 

88  40 

210.1 

18.27 

2.0 

9.0 

£  Sculptoris . . . 

40     1 

-25  39 

69.6 

5.53 

6.0 

10.0 

White :  dull  red. 

a  Piscium  .... 

55  50 

2  11 

322.2 

3.12 

2.8 

3.9 

y  Audromedte . 

66  32 

41  45 

62.4 

10.33 

3.0 

5.0 

j  Yellow  :     blue.       B 
1      again  double,  0".5. 

I  Trianguli.. . . 

2     5  25 

29  45 

80.5 

3.68 

5.0 

6.4 

Yellow  :  blue. 

t  Cassiopeae . . . 

19  10 

66  52 

265.1 

2.01 

4.2 

7.1 

A  and  B.  ) 
A  and  C.  f 

107.3 

7.62 

8.1 

84  Ceti 

35'  4 

-1  12 

324.7 

4.63 

6.0 

9.2 

Yellow  :  ashy. 

y  Ceti 

31     5 

2  44 

289.2 

2.67 

3.0 

6.8 

Yellow :  blue. 

E  Arietis 

52  21 

20  52 

201.9 

1.26 

5.7 

6.0 

Binary. 
I  Light  -  green  :    ashy. 

^  Persei 

3  46  35 

31  32 

207.6 

12.47 

2.7 

9.3 

•|      Other  small   stars 
(      in  the  field. 

E  Persei 

49  48 

39  40 

9.2 

8.81 

3.1 

8.3 

Pale-white :  lilac. 

39  Eridani 

4     8  41 

-10  33 

153.7 

6.26 

6.0 

9.1 

Yellow :  blue. 

<j>  Tauri 

12  58 

27     4 

245.5 

53.78 

5.0 

8.0 

Red :  bluish. 

p  Orionis 

5     1     1 

2  43 

63.4 

7.05 

4.7 

8.5 

Yellow :  blue. 

^      "       

8  46 

-8  20 

198.8 

9.14 

1.0 

8.0 

23     "       

16  32 

3  26 

28.1 

31.71 

5.0 

7.0 

ri        "       

18  27 

-2  30 

83.8 

1.11 

4.0 

5.0 

Discovered  by  Dawes. 

\        "       

28  32 

9  51 

40.3 

4.23 

4.0 

6.0 

Yellow :  purple. 

0'      "       

29  23 

-5  28 

Sextuple.  In  the  great 
1      nebula  of  Orion. 

a       "      

32  43 

-2  40 

236.5 

11.00 

4.1 

10.3 

A  and  B.  } 
A  and  C.  J 



84.5 

12.86 

7 

.5 

Z  Orionis 

'3442 

-2  "  0 

151.3 

2.55 

2.0 

5.7 

Yellow  :  light-purple. 

1 1  Monocerotis. 

6  23     0 

-6  57 

130.0 

7.25 

5.0 

5.5 

A  and  B.  ) 
B  and  C.  \ 

.... 

101.7 

2.46 

6.0 

12  Lyncis 

35  38 

59  34 

153.7 

1.53 

5.2 

6.1 

A  and  B.  [ 

304.2 

8.67 

7.4 

A  and  C.  \ 

Aa 


536 


APPEXDIX. 


56  Aurigae . . . 
fi  Canis  Maj. . 
d  Geminoruin 

Castor 

5  Xavis 

^  Cancri 


38  Lvncis. . . . 
y  Leonis  . .  .  . 
35  Seitantis . 
5  Ursae  Maj.  . 
65  Ursae  Maj. 

Q  Comae 

•2i     "     

y  Virginis  .  . . 
35  Comae . . . . 


84  Virginis . 
^  Bootis 


d  Serpentis 
I  Librae . . . 


Antares .... 
36  Ophiuchi 
a  Herculis . . 

P  "  •• 
70  Ophiuchi 
£*  Ljnrae  .... 


12  Aquarii. . 
61  Cvgni . .  . 
/3  Cephei . . . 
41  Aquarii.. 
53         "     .. 

y  " 

^  "      .. 

(T  Cassiopeae 


Right  Atceo.  Declination 
IS80.  1880. 


i.    M.     S. 

33  5 
50  36 
Y  12  57 
26  57 
42  19 

8  5  19 

9  11  23 

10  13  20 
37 

11  11  48 
48  51 

58  8 

12  29  6 
35  36 
47  23 

13  37  2 

14  35  25 
39  45 
45  51 

59  51 

15  19  58 

29  5 
57  46 


18 


Potiti'D 
Angle. 


43    42      17.1 

-13  53i343.5 
22  121196.9 
32     9J239.3 

-11  64    17.5 

18  1130.1 

132.0 

37  19  240.2 

20  27  111.2 
5  23J240.5 

32  13  317.6 

47  91  36.4 

22  81240.6 

19  2|271.9 
—  0  47;i59.3 

21  54i  25.3 
....     |l24.7 

4     9  235.3 


/3Cygni 19 

Z  Sagittae . 
£  Draconis 
9  Sagittae . 
49  Cygni . 
c  Equulei . 


20 


21 


22 


23 


22  2 
7  59 
9  10 

19  33 
59  23 
40  22 
40  24 
40  38 
25  53 
43  39 
48  34 

4  39 
36  11 
53  5 

57  44 
1  14 

27  6 
7  40 

20  3 
22  39 

9  35 
62  66 


14  15 
27  35 

19  36 
48  7 
37  48 

10  56 
-11  3 

-26  10 

-26  25 

14  32 

37  15 

2  33 
39  33 
39  29 
37  29 
27  42 
18  51 

69  58 

20  33 
31  63 

3  60 

-6  18 
38 

70  2 
-21  40 
-17  21 

-0  38 
-9  44 
55 


Ma^itndea. 


303.2 
320.6 
301.6 
239.8 
171.9 
141.9 
196.9 
173.1 

70.3 
268.7 
227.3 
118.5 
307.2 

83.7 

26.0 
155.2 
149.7 

65.7 
312.8 
354.5 
326.7 

49.4 
283.9 

76.2 
189.6 
115.6 
250.0 
119.4 
304.5 
334.6 
312.2 
323.4 


55.38  6.0 

3.22  4.7 

7.14  3.2 

5.49 

3.32 

0.74 

5.48 

2.69 

3.18 

6.72 

1.09 

3.71 

3.73 
20.42 

4.77 

1.43 
28.60 

3.39 

1.02 

2.63 

6.44 

4.80 
108.46 

0.69 


2.7 
5.3 

5.0 
I 

4.0* 
2.0 
6.1 
4.0 
6.0 
6.0 
4.7 
3.0 
5.0 
< 

5.8 
3.5 
3.0 
4.7 
5.2 


5.5 


9.0 
8.0 
8.2 
3.7 
7.4 
5.7 

6.7 
3.5 
7.2 
4.9 
8.3 
7.5 
6.2 
3.< 


9.0 


8.2 
3.9 
6.3 
6.6 
6.1 


White :  blue. 


A  and  B. 
A  and  C. 


Yellow 
Yellow 
Binary. 
Yellow 


greenish, 
blue. 

blue. 


Binarv. 
A  and  B. 
A  and  C. 
Yellow  : 


blue. 


6.7 
2.56[3.0 
1.06  4.9 
7.05  ' 
3.46|l.O 
5.55i6.0 
4.65  3.0 


Yellow :  blue  or  green. 

Yellow:  reddish  purple. 

Yellowish  :  bluish. 
4.0       A  and  B.  }  Binarv 
7.3  B  and  C.  f 
4.0  ^Binary. 
5.2 1 A  and  B.  )  Binary. 

A  and  C.  f 
7.0  Red :  green. 


4.0 
4.1 
4.6 
4.9 
4.2 
3.0 


3.60 

3.48 

3.03 

2.57 
43.71 
34.29 

8.49;6.7 

2.7914.0 
11.40  6.0 

2.74 

0.06 
10.83 

2.66 
19.65 
13.57 

4.08 

8.20 

3.40 
49.63 

3.01 


6.0 

5.2 

I 

5.6 
5.3 
3.0 
6.0 
6.0 
4.0 
4.5 
5.4 


7.1 


6.0 
6.1 
6.1 
6.1 
6.3 
5.2 
5.5 
5.3 
8.8 
7.6 
8.3 
8.1 
6.2 

7.7 
5.9 
8.0 
8.5 


Yellow :  emerald. 
Yellow :  purple.  Binary, 


Golden  yellow :  blue. 
Light-green :  blue. 
Yellow :  blue. 


Yellow:  blue. 
A  and  B. 
A,  B,  and 
Yellowish :  blue. 


idC.  \ 


Light-green:  blue. 

Yellow :  blue. 

White :  yellow. 
4.1  Binary. 
8.5  Yellow:  blue. 
7.5  White:  blue. 


Note.— The  sign  minus  (— )  before  declinations  means  south;  without  the  sign,  it  i$ 


LIST  OF  NEBULA  AND  STAB  CLUSTERS. 


537 


III. 


LIST  OF  THE  MORE  INTERESTING  AND  REMARKABLE  NEBULA  AND 
STAR  CLUSTERS. 


Object. 

R.  A.  1880. 

Dec.  1680. 

47  Toucani  cluster 

H.    M. 
0    19 

0  36 
0  42 
3  29 

3  39 

4  15 

5  9 
5    10 
5   29 
5   30 
5   30 
5   39 
7   36 

7  48 

8  45 

9  11 
9   18 
9  45 

10     2 

10  19 

11  8 

12  13 
12   17 
12  34 

12  36 

13  7 
13   18 
13   20 
13   25 
13  30 
13  32 
13   37 

o        ' 

72  45  S. 
40  37  N. 
25   57  S. 
36  32  S. 
23  23  N. 
19   14  N. 

68  55  S. 
40  11  S. 

5  29  S. 

21     8  N. 

1   17  S. 

69  10  S. 

14  32  S. 
88   13  S. 
12   15  N. 
36     7S. 
57  47  S. 
69   38  N. 
39   51  S. 
18     2  S. 
55  40  N. 

15  5  N. 

16  29  N. 
10  57  S. 
33   12  N. 
18  48  N. 
42  23  S. 

46  41  S. 

47  49  N. 
29   16  S. 

17  16  S. 
28   59  N. 

Great  nebula  of  Andromeda 

Nebula 

t( 

Tempel's  variable  nebula 

Hind's  variable  nebula.         

Globular  cluster 

Great  nebula  of  Orion 

Chacornac's  variable  nebula 

Nebula  around  £  Orionis 

Looped  nebula 

Cluster  and  nebula  Mess.  46 

Star  cluster 

"        "       Mess.  67 

Planetary  nebula 

Nebula 

Planetary  nebula 

u                  a 

Spiral  nebula 

Nebula 

(( 

Bifid  nebula 

Spiral  or  ring  nebula 

Spiral  nebula 

Cluster 

538 


AFPENDIX. 


Object. 

R.  A.  IsSO. 

Dec.  1880. 

Cluster 

H.    M. 

15   12 

15  38 

16  10 
16  37 
16  41 
16  51 
16  52 

16  54 

17  14 
17   22 
17  31 
17  55 

17  57 

18  14 
18  29 

18  49 

19  5 

19  54 

20  11 
20  17 
20  40 

20  58 

21  27 
21   34 
23   20 

2  33  N. 

37  23  S. 

22  41  S. 
36  42  N. 

1  44  S. 

3  54  S. 
44  29  S. 

29  56  S. 

38  21  S. 

23  39  S. 
3   10  S. 

23  2S. 

24  21  S. 
16   13  S. 
24     OS. 
32  53  N. 

0  50  N. 

22  24  N. 

30  12  N. 
19  44  N. 
30  17  N. 
11   50  S. 

1  22  S. 

23  43  S. 
41   53  N. 

«i 

Resolvable  nebula 

Great  Cluster  of  Hercules 

Cluster 

(1 

(1 

i( 

Small  annular  nebula 

((          11           11 

Cluster 

Trifid  nebula 

Nebulous  cluster 

Hooked  nebula 

Cluster 

Annular  nebula  of  Lyra 

Variable  nebula 

Dumb-bell  nebula 

Small  annular  nebula 

Planetary  nebula 

Nebula  around  k  Cvgni 

Planetary  nebula 

Cluster 

Blue  planetary  nebula 

To  facilitate  the  finding  of  the  above  nebulte  and  clusters^  their  posi* 
tioQS  are  marked  on  the  star-maps  -^ith  small  circles. 


PERIODIC  COMETS  SEEN  AT  MORE  THAN  ONE  RETURN.  539 


1 

1 

«2         3         0         *         0 

s    >-s    0    a    0 

^      a.               >       &• 

1 

w 

»o       5o       -^jt        10       cc 

00          10          (M          CO          CO 

^ 

00        00        00        00        00 

00          00          t-H          00          00 

CO          00          00          00          00 

00          00          Cd          00          QO 

i 

10 

H 

g     00          M          1-1 

0         CO 

« 

«OT»<ia500»C^r-IOOOOO 

'ts 

^    CO        to        »o        0        i»        0        tC       i^       0        <M        0 

•*: 

cooo«o<doir»cocoiOkO 

(S 

■-I        i:- 

a 

*  5  J 

^     a: 

(M          »0          IS 

C 

cc 

10       t-       cc 

t-       CO         1 

>c 

•- 

0       CQ 

rt      ■<* 

•^ 

rH 

s  1 J 

ec 

>c 

Tt 

a- 

cc 

cc 

0          cc 

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APPENDIX. 


VI. 


ELEMEXTS  OF  THE  SMALL  PLAXETS. 

COitPILED    BY    D.  P.  TODD. 


Sign  asd  Nam*. 


(1)  Ceres 

(2)  Pallas.... 

(3)  Juno 

(4)  Vesta 

(5)  Astrxa... 

(6)  Hebe 

(T)  Iris 

(S)  Flijra 

(9)  MeWs 

(10)  Hygeia... 

(11)  Parthenope . 

(12)  Victoria 

(13)  Egeria 

(14)  Irene 

(15)  Eunomia — 

(16)  Psyche 

(17)  Thetis 

(18)  Melpomene. . 

(19)  Fortuna 

(20)  Massalia  — 

(21)  Lntetia 

(22)  Calliope 

(23)  Thalia 

(24)  The  mis 

(25)Phocaea 

(26)  Proserpine . . 

(27)  Euterpe 

(28)  Bellona 

(29)  Amphitrite.. 

(30)  Urania 


1801 
1S02 
1804 
1807 
1845 

1847 

1847 
1847 
1848 
1&49 

1850 
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1850 
1851 
1851 

1852 
1852 
1S52 
1852 
1852 

1852 
1852 
1852 
1853 
1853 

1853 
1853 
1864 
1854 
1854 


Piazzi 

Olbers 

Harding 

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Hencke , 

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Hind 

Graham 

Gasparis.  — 

Gasparis 

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Gasparis 

Hind 

Gasparis 

Gasparis 

Luther 

Hind 

Hind 

Gasparis 

Goldschmidt. 

Hind 

Hind 

Gasparis 

Chacornac... 

Luther. 

Hind 

Luther 

Marth 

Hind 


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2.34 

869.0 

4.09 

0.074 

56.4 

356.7 

2.66 

2.06 

975.4 

3.64 

0.127 

32.1 

308.1 

10.6 
34.7 
13.0 
7.1 
6.3 

14.8 
6.5 
6.9 
5.6 
3.8 

46 

8.4 
16.5 

9.1 
11.7 

3.1 
5.6 

10.2 


3.1 
13.7 
10.2 

0.8 
21.6 

3.6 
1.6 
9.4 
6.1 
2.1 


2.769 
2.771 
2.66S 
2.361 
2.579 

2.424 
2.886 
2.201 
2.387 
3.144 

2.452 
2.334 
2.577 
2.691 
2.644 

2.921 
2.473 
2.296 


1.5  I  2.442 
0.7    2.409 


2.435 
2.909 
2.629 
3.136 
2.400 

2.666 
2.347 
2.777 
2.625 
2.365 


ELEMENTS  OF  THE  SMALL  PLANETS. 


543 


Si^  and  Name. 


(31)  Euphrosyne . 

(32)  Pomona 

(33)  Polyhymnia. 

(34)  Cii-ce 

(38)  Leucothea... 

(36)  Atalanta  .... 

(37)  Fides 

(3S)Leda 

(89)  Laetitia 

(40)  Harmon  la. .. 

(41)  Daphne 

(42)Isis 

(43)  Ariadne 

(44)  Nysa 

(45)  Eugenia 

(46)  Hestia 

(47)  Aglaia 

(48)  Doris 

(49)  Pales 

(50)  Virginia 

(51)  Nemausa — 

(52)  Enropa 

(53)  Calypso 

(54)  Alexandra... 

(55)  Pandora 

(56)  Melete 

(57)  Mnemosyne. 

(58)  Concordia, . . 
(59)Elpis 

(60)  Echo 

(61)  DanaG 

(62)  Erato 

(63)  Ausonia 

(64)  Angelina. . . . 

(65)  Cybele  . . . 

(66)  Maia 

(67)  Asia 

(68)  Leto 

(69)  Hesperia . 

(70)  Panopaea. 

(71)  Niobe .... 

(72)  Feronia . . 
(73)C)ytia.... 

(74)  Galatea. . . 

(75)  Eurydice. 


1854 
1854 
1854 
1855 

1855 

1855 
1855 
1S5G 
185G 
1856 

1856 
1856 
1857 
1857 
1857 

1857 
1857 
1857 
1857 
1857 

1858 

1858 
1S58 
1858 
1858 

1857 
1859 
1360 
1800 
ISGO 

18G0 
18G0 
1361 
1861 
1861 

1861 
1861 
1801 

18G1 
1861 

1861 
1861 
1862 
1862 
1862 


Ferguson 

Goldschmidt. 

Chacornac 

Chacornac 

Luther 

Goldschmidt 

Luther 

Chacornac 

Chacornac. . 
Goldschmidt... 

Goldschmidt... 

Pogsou 

Pogson 

Goldschmidt... 
Goldschmidt... 

Pogson 

Luther 

Goldschmidt... 
Goldschmidt... 
Ferguson 

Laurent  

Goldschmidt... 

Luther 

Goldschmidt... 
Searle 

Goldschmidt. . . 
Luther  .... 

Luther 

Chacornac. 
Ferguson.. 

Goldschmidt. . . 

Foerster 

Gasparis 

Tempel , 

Tempel , 

Tuttle 

Pogson 

Luther 

Schiaparelli. . 
Goldschmidt. 

Luther 

Peters 

Tuttle 

Tempel 

Peters 


1  i 

o5 

§  § 
a 

If 

Yre. 

3.85 

2.45 

035.3 

5.59 

2.80 

2.37 

852.6 

4.1C 

3.83 

1.89 

733.3 

4.84 

2.97 

2.40 

805.8 

4.41 

3.66 

2.32 

685.0 

5.18 

3.57 

1.92 

TSO.O 

4.55 

3.11 

2.17 

826.4 

4..S0 

3.16 

2.32 

782.1 

4.54 

3.08 

2.4G 

769.8 

4.61 

2.37 

2.1G 

1039.3 

3.42 

3.51 

2.02 

773.3 

4.59 

2.99 

1.89 

930.9 

3.81 

2.57 

1.83 

10S5.0 

3.27 

2.79 

2.06 

940.5 

3.78 

2.94 

2.50 

791.0 

4.49 

2.94 

2.11 

SS4.0 

4.02 

3.25 

2.50 

725.9 

4.89 

3.33 

2.89 

646.4 

5.49 

3.81 

2.36 

655.3 

5.42 

3.41 

1.90 

821.6 

4.32 

2.52 

2.21 

975.4 

3.64 

3.35 

2.70 

651.2 

5.45 

3.15 

2.08 

836.5 

4.25 

3.25 

2.17 

795.G 

4.46 

3.15 

2.37 

774.0 

4.59 

3.2a 

1.98 

848.1 

4.19 

3.50 

2.81 

633.0 

5.61 

2.81 

2.59 

799.0 

4.44 

3.03 

2.40 

794.0 

4.47 

2.83 

1.95 

958.3 

3.70 

3.47 

2.50 

6S7.5 

6.16 

3.67 

2.59 

640.9 

5.54 

2.69 

2.10 

955.0 

3.72 

3.02 

2.34 

808.3 

4.39 

3.80 

3.05 

558.9 

6.35 

3.09 

2.21 

824.6 

4.32 

2.S7 

1.97 

941.5 

3.77 

3.30 

2.20 

705.3 

4.64 

3.49 

2.47 

089. 9 

5.15 

3.09 

2.14 

839.6 

4.23 

3.23 

2.28 

775.4 

4.58 

2.54 

1.99 

1040.1 

3.41 

2.78 

2.55 

815.4 

4.35 

3.44 

2.12 

765.6 

4.64 

3.49 

1.85 

812.3 

4.37 

td 


0.223 
0.083 
0.340 
0.107 
0.224 

0.302 
0.177 
0.154 
0.111 
0.047 

0.270 
0.226 
0.167 
0.151 
0.082 

0.165 
0.130 
0.071 
0.235 
0.285 

0.067 

0.109 
0.204 
0.199 
0.142 

0.23G 
0.109 
0.042 
0.117 
0.184 

0.162 
0.173 
0.124 
0.128 
0.110 

0.105 
0.186 
O.ISS 
0.170 
0.183 

0.173 
0.120 
0.042 
0.238 
0.306 


93.4 
193.4 
342.4 
148.7 
202.4 

42.9 

66.5 

101.2 

3.2 

0.9 

220.0 
318.0 
278.0 
112.2 
229.0 

354.2 

312.8 
70.3 
31.6 
10.1 

175.2 

107.1 
93.0 

294.3 
12.1 

294.0 
54.1 

189.2 
13.4 
98.6 

344.1 

38.5 
270.4 
123.7 
260.8 

46.4 
306.4 
345.2 

108.5 
299.8 

221.3 

308.0 

57.9 

8.6 

335.5 


31.5 

220.7 

9.2 

184.8 

355.8 

359.4 

8.3 

296.4 

157.4 

93.6 

179.2 
8^.5 
264.9 
131.1 
148.2 

181.5 
4.3 
135.2 
290.7 
173.8 

176.9 

129.7 

144.0 

313.8 

10,9 

194.1 
200.2 
161.4 
170.4 
192.1 

334.2 
125.7 
338.0 
311.3 
158.8 

8.3 
202.S 

45.0 
187.2 

4S.3 

316.5 

207.S 

7.9 

197.9 

3.W.9 


26.5 
5.5 
1.9 
5.4 

8.2 

IS.  7 
3.1 
7.0 

10.4 
4.3 

16.0 
8.6 
3.5 
3.7 
6.6 

2.3 
5.0 
6.5 

3.1 
2.8 

10.0 

7.4 
5.1 
11.8 
7.2 

8.0 
15.2 
5.0 
8.0 
3.6 

18.2 
2.2 
5.8 
1.3 
3.5 

8.1 
6.0 
8.0 
8.5 
11.6 

23.3 
54 
2.4 

4.0 
5.0 


3.148 
2.587 
2.861 
8.696 
i994 

2.745 
2.642 
2.740 
2.770 
2.267 

2.761 
2.440 
2.203 
2.423 
2.720 

2.620 

2.880 
3.112 
3.084 
2.652 

2.365 
3.026 
2.620 
2.709 
2.760 

2.596 
3.155 
2.700 
2.713 
2.393 

2.987 
3.130 
2.393 
2.681 
3.428 

2.650 
2.422 
2.781 
2.980 
2.614 

2.786 
2.266 
2.Co5 
2.780 
2.672 


3t) 


544 


APPENDIX. 


Sifj^  and  Name. 


(76)  Freift 

(TV)  Frigga 

(78)  Diana 

(79)  Eurynome. . 

(50)  Sappho 

(51)  Terpsichore 
(32)  Alcmene  . . . 

(83)  Beatrix..... 

(84)  Clio 

(86)  lo 

(86)  Semele 

(S7)  Sylvia 

(S3)  Thisbe 

(89)  Julia 

(90)  Antiope.... 

(91)  iEgina 

(92)  Undina.... 

(93)  Minerva.... 

(94)  Aarora.... 
(96)  Arethnsa... 

(96)  ^gle 

(9T)  Clotho 

(95)  lanthe 

(99)  Dike 

(100)Hekate 

(101)  Helena 

(102)  Miriam 

(103)  Hera 

(104)Clymene... 
(105)  Artemis.... 

(106)DioDe 

(107)  Camilla.... 

(lOS)  Hecaba 

(109)  Felicitas  . . . 
(llO)Lydia 

(111)  Ate 

(112)  Iphigenia .. 

(113)  Amalthea.. 

(114)  Cassandra.. 
ai5)Thyra 

(116)Sirona. 

(117)  Lomia 

(llS)Peitho 

(119)  Althaea 

(120\Lache3i3.... 


1S62 
1S62 
1S63 
1363 
1S64 

1S64 
1S64 
18C5 
1S65 
1S66 

1366 
1S66 
1SC6 
1S66 
1366 

1S66 
1367 
1S67 
1SC7 
1867 

1868 
1S6S 
1S6S 
1868 
1S6S 

1S68 
18C8 
1S6S 
1S6S 
1363 

1S68 
136S 
1369 
1SC9 
ISTO 

1870 
1S70 
1871 
1871 
1S71 

1S71 
1871 
1372 

1872 
1S72 


D*  Arrest 
Peters... 
Lnther  . . 
Watson  . 
Pogson , . 

Temple.. 
Luther. . . 
Gasparis. 
Luther. . . 
Peters... 

Tietjen . . 
Pogson . . 
Peters... 
Stephan . 
Luther . . 

Stephan . 
Peters... 
Watsou.. 
Watson . . 
Luther. . . 

Coggia . . 
Tempel.. 
Peters . . . 
Borelly.. 
Watsou. . 

Watson.. 
Peters... 
Watson.. 
Watson. . 
Watson. . 

Watson.. 
Pogson . . 
Luther . . . 

Peters 

Borelly... 

Peters 

Peters 

Luther . . . 

Peters 

Watson.. 

Peters 

Borelly. ., 
Luther  . . , 
Watsou.., 
Borellv.., 


4.00 
3.03 
3.16 
2.92 
2.76 

3.45 
3. 38 
2.64 
2.92 
3.16 


3.21 
3.01 
3.68 


3.51 
8.14 
3.44 
3.52 

3.48 
3.36 
3.20 
3.46 


2.94 
3.47 
2.92 
3.70 
2.79 

3.73 
4.00 
3.54 
3.50 
2.94 


2.S2 
2.31 
2.03 
1.97 
1.S4 

2.25 
2.15 
2.22 
1.80 
2.15 


3.76    2.46 
3.76  i  3.21 


2.S7    2.31 


2.32 
2.09 
2.61 


2. 86 
2.37 
2.89 
2.63 

2.62 
1.98 
2.18 
2.13 


3.60    2.5S 


2.23 
1.86 
2.48 
2.60 
1.96 

2.59 
3.12 
2.SS 
1.89 
2.62 


2.86  2.32 
2.74  2.12 
2.5S    2.17 

3.05  ;  2.30 
2.S4  1 1.92 

3.16  j  2.37 

3.06  i  2.92 
2.83  j  2.05 
2.79  i  2.36 
3.27    2.97 


563.7 
812.2 
835.3 
928.9 
1019.8 

736.2 
771.4 
936.7 
976.9 

820.7 

646.3 
546.0 
770.2 
870.8 
636.2 

S51.S 
623.7 
776.5 
630.7 
657.7 

666.2 
814.2 
804.S 
753. 7 
652.5 

854.2 
817.0 
799.1 
635.0 
970.1 


1  ^ 

1 

Yrs. 

6.30 

0.174 

4.37 

0.134 

4.25 

0.205 

3.S2 

0.194 

3.48 

0.200 

4.S2 

0.211 

4.60 

0.221 

3.79 

0.086 

3.63 

0.236 

4.33 

0.191 

5.49 

0.210 

6.50 

0.079 

4.61 

0.160 

4.08 

0.180 

5.58 

0.169 

4.17 

0.108 

5.69 

0.102 

4.57 

0.140 

5.63 

0.086 

5.40 

0.144 

5.33 

0.140 

4.36 

0.25S 

4.41  I  0.1S9 
4.6S  0.238 
5.44    0.164 


4.16 
4.35 


631.6 

6.C2 

528.2 

6.72 

616.4 

5.76 

802.0 

4.43 

785.4 

4.62 

849.9 

4.1S 

934.7 

3.80 

96S.S 

3.66 

810.6 

4.33 

966.9 

3.C7 

770.9 

4.60 

CS6.0 

6.  IS 

931.9 

3.81 

855.0 

4.16 

643.5 

6.52 

0.138 
0.303 


4.44  O.OSO 
5.69  0.174 
3.66    0.175 


0.181 
0.123 
0.103 
0.300 
0.077 

0.105 
0.128 
0.087 
0.140 
0.194 

0.143 
0.023 
0.161 
0.083 
0.047 


92.3 
60.4 

121.3 
44.4 

355.3 

48.7 
132.4 
191.8 


212.2 

2.0 

334.1 

206.7 

21S.7 

2.7 
27.0 
27.5 


339.3  :  327.5 
322.6    203.9 


29.7  83.1 

335.4  1  76.1 

309.3  !  277.6 

353.4  311.7 
301.1  71.4 


80.3 
330.8 
274.7 
46.0 
31.2 


11.1 

102.9 

5.1 

4.6 

844.3 


327.4 
354.6 
321.0 
58.2 
242.8 

27.0 
112.8 
173.5 

66.0 
336.8 

108.7 
338.2 
198.7 
153.1 
43.0 

152.8 
4S.S 
77.6 
12.4 

214.0 


343.7 
212.0 
130.3 
44.0 
1SS.0 

63.4 

175.7 

352.4 

4.9 

57.2 

306.2 
324.0 
123.2 
161.4 
309.1 


2.0 
2.6 
8.6 
4.6 
8.6 

7.9 
2.9 
6.0 
9.4 
11.9 

4.S 
10.9 

5.2 
16.2 

2.3 

2.1 
9.9 

8.6 

8.1 

12.9 


163.2  322.8  16.1 
65.6  160. 7  ,  11.8 
147.6  ;  354.4  i  15.6 

240.6  j    41.7  1  13.9 

307.7  123.2  I    6.4 


10.2 
5.1 
6.4 
2.9 

21.6 

4.6 
9.8 
4.4 
8.0 
6.0 

4.9 
2.6 
5.0 
4.9 
11.6 


64.4  3.6 
349.6  ;  15.0 

47.5  7.8 
204.0  6.S 
342.9  I    7.0 


ELEMENTS  OF  THE  SMALL  PLANETS. 


545 


(121 
(122 
(123 
(124 
(125; 

(126; 
(127 

(12S 
(129 

(i3o; 

(131 
(132 
(133; 

(134: 
(135: 

(i3o: 

(13T 
(138: 
(139 

(i4o; 

(141 
(142: 
(143: 

(144: 

(145; 

(146; 
(147 
(148; 

(149; 
(150; 

(151 

(152; 

(153 

(154; 
(155; 

(156; 
(157; 
(168; 
(159; 
(ico; 

(161 

(162; 

(163 

(164; 
I  (1C5; 


■n  and  Name. 

°  t 

-5 

Ilermioue. . 

1S72 

Gei-da 

1ST2 

Briiiihilda.. 

1872 

Alccste 

1872 

Libcratrix. . 

1872 

Velleda 

1872 

Johaima.... 

1872 

Nemesis... . 

1872 

Antigoue. . . 

1873 

Electra 

1873 

Vala 

1873 

^ihra 

1873 

Cyrene 

1873 

Sophrosyne. 

1873 

Hertha 

1874 

Austria 

1874 

Meliboea.... 

1874 

Tolosa 

1874 

.Jiiewa 

1874 

Siwa 

1874 

Lumen 

1875 

PoliUia 

1875 

Adria 

1875 

Vibilia 

1875 

Adeoua .... 

1875 

Lncina 

1875 

Protogeneia 

1875 

Gallia 

1875 

Medusa 

1875 

Nuwa 

1875 

AbundaiUia. 

1S75 

Atala 

1875 

Hilda 

1875 

Bertha 

1875 

Scylla 

1875 

Xantliii)i)e.. 

1875 

Dfjaiiiia.... 

1875 

Coi-oiiis 

1S76 

.^Emilia...  . 

1S7C 

1876 
1876 

Athoi- 

Laurentia . . 

1876 

Erigoue 

1876 

Eva 

1876 

Loreley 

1876 

Watson 

Peters 

Peters 

Peters. 

Prosper  Ueury. 

Paul  Ilenry 

Prosper  Henry. 

Watsou 

Peters 

Peters 

Peters 

Watsou 

Watsou 

Luther 

Peters 

Palisa 

Palisa 

Perrotiu 

Watson 

Palisa 

Paul  Henry — 

Palisa 

Palisa 

Peters 

Peters 

Borelly 

Schulhof. 

Prosper  Ueury. 

Perrotiu 

Watson 

Palisa 

Paul  Henry 

Palisa 

Prosper  Hcury. 
Palisa 

Palisa 

Borelly 

Kuorre 

Paul  Uenry 

Peters 

Watson 

Prosper  Henry. 

Perrotiu 

Paul  Henry 

Peters 


3.89 
3.34 
3.02 
2.83 
2.96 

2.70 
2.04 
3.10 
3.47 
3.77 

2.62 
3..59 
3.4S 
2.87 
2.93 

2.48 
3.78 
2.S5 
3.27 
3.32 

3.23 
2.74 
2.90 
3.27 
3.00 

2.91 
3.22 
3.2S 
2.39 
3.37 

2.08 
3.41 
4.03 
3.40 
3.06 

3.84 
3.13 
3.02 
3.45 
2.90 

2.69 
3.56 
2.72 
3.35 
3.36 


3.02 
3.09 
2.37 
2.43 
2.53 

2.18 
2.59 
2.40 
2.28 
2.47 

2.22 
1.00 
2.63 
2.26 
1.93 

2.09 
2.48 
2.05 
2.29 
2.14 

2.10 
2.10 
2.50 
2.03 
2.33 

2.53 
3.06 
2.26 

1.88 
2.59 

2.50 
2.86 
3.27 
2.92 

2.17 

2.24 
2.04 
2.72 
2.77 
2.56 

2.05 
2.49 
1.09 

1.72 
2.89 


551.6 
615.6 

801.8 
S32.0 
780.7 

931.0 
775.3 
777.5 
727.2 
C42.9 

942.3 
S46.4 
C03.G 
864.6 
93S.1 

1026.4 
041.9 
926  0 

705.8 
786.1 

814.5 
942.9 
773.0 
S21.3 

815.4 

789.9 
C3S.7 
769.5 
1139.2 
CS9.3 

S50.7 
039.0 
451.0 
022.4 
713.8 

670.2 
8.'54.8 
730.6 
647.7 

787.2 

970.0 
073.1 
981.1 
829.7 
042.1 


Yrs. 

0.43 
5.76 
4.42 
4.26 
4.54 

3.81 
4.58 
4.50 
488 
5.52 

3.77 
4.19 
5.35 
4.10 
3.78 

3.46 
5.53 
3.S3 
4.03 
4.51 

4.30 
3.70 
4.59 
4.32 
4.35 

4.49 
5.55 
4.01 
3.11 
5.15 

4.17 
5.55 

7.S6 
5.70 
4.97 

5.29 
4.15 

4.80 
5.48 
4.51 

3.06 
5.27 
3.62 
4.28 
5.53 


a 


0.125 
0.040 
0.122 
0.077 
0.077 

0.107 
0.067 
0.128 
0.208 
0.208 

0.081 
0.383 
0.140 
0.118 
0.205 

0.0S4 

0.208 
0.102 
0.177 
0.217 

0.211 
0.132 
0.073 
0.235 
0.12C 

0.070 
0.026 
0.185 
0.119 
0.131 

0.036 
0.087 
0.172 
0.084 
0.250 

0.204 
0.2U 
0.053 
0.110 
0.062 

0.136 
0.177 
0.150 
0.347 
0.070 


358.6 
204.5 
70.0 
244.8 
272.9 

347.8 

120.0 
1G.8 

241.8 
20.5 

257.9 
152.6 
247.2 
67.5 
319.9 

316.1 
30S.0 
311.4 
164.6 
300.3 

13.9 

219.9 

222.5 

7.2 

118.5 

210.1 

2G.0 

30.1 

246.7 

357.1 

167.3 

84.9 

285.S 

184.4 

82.0 

156.0 
107.4 

58. 0 
101.3 

56.0 

313.3 

145.8 
93.8 
3.')9.0 
2T7.0 


70.S 
178.7 
SOS.  5 
188.4 
169.5 

23.1 
31. S 
76.5 
187.9 
140.0 

65.3 
259.7 
321.1 
340,4 
343.9 

186.1 

204.4 

54.8 

2.4 

107.1 

319.1 
202.3 
3.33.7 

76.8 
77.7 

84.2 
251.2 
14.^2 
lOO.l 
207.6 

3S.9 
41.6 
228.3 
37.7 
42.9 

246.2 
62.5 
281.2 
135.2 
9.4 

IS.  6 
38.2 

159.1 
77.5 

304.1 


7.0 
1.0 
6.4 
2.9 
4.6 

2.9 
S.3 
6.3 
12.2 
22.9 


J| 


3.459 
3.215 
2.695 
2.630 
2.744 

2.440 
2.766 
2.751 
2.876 
3.123 


4.6    2.420 
24.9    2.600 

7.2  j  3.058 
11.6    2.563 

2.3  2.42S 


9.6 
13.4 

3.2 
11.0 

3.2 

12.0 
2.2 

11.5 
4.8 

12.3 

13.2 
1.9 

25.4 
1.1 
2.1 

6.5 
12.2 

7.9 
21.0 
14.1 

7.5 
12.0 
1.0 
6.1 
3.9 

9.2 

6.2 

4.7 

24.4 

11.2 


2.286 
3.126 
2.449 
2.779 
2.731 

2.667 
2.419 
2.762 
2.653 
2.665 

2.722 
3.137 
2.770 
2.133 

2.981 

2.591 
3.136 
3.952 
3.191 
2.913 

3.038 
2.583 
2.868 
3.107 
2.729 

2.374 
3.029 
2.356 
2.635 
3.126 


546 


APPENDIX. 


i  - 

9        . 

Jo 

r 

1 

si 

o 

o 

o 

30.9 

129.6 

12.0 

2.693 

32.7 

170.1 

1.7 

3.219 

13.0 

209.8 

4.5 

3.384 

32C.9 

354.0 

55 

2.360 

95.8 

301.3 

14.4 

2.555 

143.  C 

101.2 

2.6 

a  147 

32S.6 

331.9 

10.0 

2.380 

13.6 

14S.C 

14.2 

2.746 

253.4 

328.9 

12.2 

2.864 

293.2 

23.6 

as 

a504 

20.8 

201.2 

22.5 

a  190 

25.2 

349.0 

1.4 

2.758 

26S.2 

50.7 

1.9 

2.459 

354.9 

253.3 

7.8 

2.973 

126.6 

315.0 

0.9 

2.728 

95.8 

144.8 

1S.6 

aii9 

546 

106.5 

2.0 

2.417 

45.0 

142.8 

26.5 

2.802 

169.4 

330.3 

1.2 

aiS8 

15.8 

153.8 

23.3 

2.733 

327.2 

14.0 

13.2 

2.363 

213.6 

22.3 

10.7 

2.740 

309.7 

241.8 

11.4 

2.821 

6.8 

203.4 

52 

2.450 

105.3 

177.0 

&1 

a933 

16.4 

159.9 

11.5 

2.889 

10.6 

343.3 

0.9 

2.403 

70.0 

351.2 

11.6 

2.676 

310.7 

159.4 

18.4 

2.619 

106.8 

8.4 

7.3 

2.872 

352.3 

73.5 

7.3 

aoss 

324.8 

82.1 

8.8 

2.743 

354.8 

268.8 

9.3 

2.454 

260.  S 

90.4 

153 

a  206 

46.6 

325.4 

6.9 

2.738 

334.6 

157.1 

57 

2.677 

127.7 

137.8 

8.8 

a034 

43.4 

34S.6 

3.2 

2.739 

2575 

205.7 

as 

2.673 

21.9 

212.2 

10.7 

2.777 

217.7 

28.9 

3.8 

2.286 

233.2 

7.S 

2.0 

2.872 

s.'ias 

2.0 

7.2 

ai4s 

56.7 

32.  S 

52 

2.745 

Sj^  and  Name. 


(166)  Rhodope. 

(167)rrda 

(165)  Sibylla... 

(l69)Zelia 

(170)  Maria, ... 


(171)  Ophelia 

(172)  Baucis 

(173)  luo 

(174)  Phaedra 

(175)  Audromache, 


(176)  Idunna... 

(177)  Irnia 

(178)  Belisana. . 

(179)  Clytemnestxa 

(180)  Garamna. 

(181)  Encharis  . 

(lS2)El6a 

(183)  Istria 

(l&4)Deiopea.. 
(185)  Eunice . . . 


(186)  Celnta  . . . . 

(187)  Lamberta . 
(ISS)  Meuippe  . . 

(189)  Phthia  . . . , 

(190)  Ismene..., 


a91)Colga 

(192)  Xansicaa  — 

(193)  Ambrosia 

(194)  Prokne 

(195)  Eurjclea . . . . 


1876 
1870 
1876 
1870 
1877 

18n 
1877 
1S77 

1877 
1877 

1S77 
1877 
1S77 
1877 
1S7S 

1878 
1S78 
1S7S 
1S7S 
1S7S 

1378 
187S 
1878 
1878 
1878 

1878 
1S79 
1S79 
1879 
1879 


(196)  Philomela...  1879 

(197)  Arete j  1879 

(198)  Ampella 1 1S79 

(199)Byblis 1S79 

(200)  Dynameuc  . .  IS79 


(201)  Peuelope. 

(202)  Chryseis  . 

(203)  Porapeia  . 
(204)Callisto... 
(205) 

(206)Her6iUa... 

(207) 

(208) 

(209)  Dido 

(210) 


1879 
1879 
1879 
1879 
1879 

1879 

1879 
1879 
1S79 
1ST9 


Peters 

Peters 

Watsou 

Prosjjer  Henry 
Perrotin 


Borelly . 
Borelly. 
Borelly. 
Watsou. 
Watson. 


Peters 

Paul  Henry. 

Palisa 

Watson 

Perrotin  — 


a  27 
4.22 
3.62 
2.67 
2.72 

a51 
2.65 
a31 
a29 
4.72 

3.71 

3.40 
2.60 
3.30 

ai9 


Cottenot a  81 

Palisa 2.ST 

Palisa |H.79 

Palisa i  3.42 

Peters ;  'A.W 

Prosper  Henry  i  2.72 
Cogiria !  3.3S 


Peters . 
Peters . 
Peters . 


Petfirs.. 
Palisa . , 
Coggia . 
Peters . . 
Palisa . . 


Peters . . 
Palisa  . . 
Borelly . 
Peters . . 
Peters . . 


Palisa  . 
Peters . 
Peters . 
Palisa . 
Palisa . 

Peters. 
Palisa . 
Palisa  . 
Peters . 
Palisa  . 


3.43 
2.54 
4.57 

3.13 
2.99 
a31 
a24 

ai4 
a  10 

3.20 

aoi 
a  72 
a  10 

a  16 
a3s 

2.90 

a  14 

2.SS 


2.35 
a  02 

ass 
ai2 


2.12 
2.22 

ai4 

2.05 
2.39 

2.79 
2.11 
2.18 
2.43 
2.28 

2.07 
2.12 
2.32 
2.65 
2.26 

2.43 
1.97 
1.S2 
2.96 
2.39 

2.01 
2.10 
2.21 
2.36 
a  30 

2.65 
1.81 
1.84 
2.00 
2.61 

ao7 

2.29 
1.90 
2. 09 
2.37 

2.19 
2.79 
2.58 
2.20 
2.68 


2.22 
2.72 
2.93 
2.37 


soao 

614.5 
570.0 
9TS.5 

S6S.S 

635.5 
966.4 

780.2 
732.1 
541.0 

6226 
774.7 
920.1 


Yre. 
4.42 
577 
6.22 
a  63 
4.  OS 

5.5S 

a67 

4.55 
4.85 
6.56 

5.70 
4.5S 
a  86 


692.215.13 

787.4  j  451 

frM.o!  551 

944.0  a76 
756.4  14.69 

623.3  5.69 

753.1  4.53 

977.1    a  63 

782.4  4.53 


74S.S 
925.0 
454.1 

722.5 
952.6 
85S.3 
S36.9 
72S.9 

053.8 
781.0 


4.74 
a84 
7.  SI 

491 
a  72 
4.13 
4.24 
4.87 

543 
4.54 


922.9  I  3.84 

618.2  1  574 

783.3  4.53,  0.133 


0.214 
0.312 
0.071 
0.131 
0.064 

O.llS 
0.114 
0.205 
0.150 
0.343 

0.164 
0.233 
0.058 
0.109 
0.170 

0.220 
0.186 
0.352 
0.073 
0.127 

0.151 
0.235 
0.217 
0.036 
0.161 

0.0S2 
0.246 
0.2S5 
0.237 
0.092 

0.005 
0.165 
0.226 
0.162 


809.9 
655.0 
782.  S 
S12.0 
766.7 


1027.4 
729.1 
637.1 
780.0 


438  0.182 
542  '  0.097 
453  0.059 
437  0.176 
463    0.035 


a  45 
487 
557 
455 


0.030 
0.051 
0.0C7 
0.136 


ELEMENTS  OF  THE  SMALL  PLANETS. 


547 


Sign  and  Name. 

1  § 
5 

Discoverer. 

1  1 
51 

Q 

II 

] 

2.  ~ 

2   5 

= 

a  S 

(211) 
(212) 

(213)Lil8ea 

(214) 

(215)  CEnoue 

(216) 

(217)  Endora 

(21S) 
(219) 
(220) 

1ST9 

ISSO 
ISSO 
ISSO 
ISSO 

ISSO 

ISSO 
ISSO 
ISSO 
18S1 

3.51 
3.41 
3.14 
2.C9 
2.88 

3.60 
4.09 
2.95 
2.94 

2.5S 
2. 82 
2.35 
2.53 
2.66 

1.99 
2.01 
2.3T 
1.83 

66T.3 
644.9 

779,8 
840.9 
770.5 

759.7 
CG5.S 
817.3 
965.4 

Yrs. 
5.32 
5.50 
4.55 
4.22 
4.60 

4.67 
5.33 
4.34 
3.6S 

0.153 
0.094 
0.144 
0.031 
0.039 

0.2S7 
0.340 
0.108 
0.230 

74.2 

62.4 

284.3 

115.9 

340.4 

35.9 
307.2 
228.7 
339.0 

265.5 
315.0 
122.6 
342.5 
25.4 

214.9 
164.1 
171.0 
200.8 

3.8 
4.2 
6.8 
3.4 
1.7 

13.8 
11.1 
15.1 
11.1 

3.046 
3.116 
2.746 
2.611 
2.768 

2.794 
3.051 
2.661 
2.3S2 

Palisa 

Peters 

Kuone 

Palisa 

Piilisa 

Palisa 

REMARKS  ON  THE  PRECEDING  ELEMENTS  OF  THE  PLANETS. 

Masses. — The  masses  of  many  of  the  planets  are  still  very  tmcertaiu, 
because  exact  observations  have  not  yet  been  made  long  enough  to  per- 
mit of  their  satisfactory  determination.  The  mass  of  Mercury  may  be 
estimated  as  uncertain  by  ^  of  its  entire  amount ;  that  of  Mars  by  -^^ ; 
that  of  Venus  by  ^^ ;  those  of  the  Earth,  Uranus,  and  Neptune  by  ^^^ ; 
while  those  of  Jupiter  and  Saturn  are  probably  correct  to  jo^oo • 

The  value  of  the  earth's  mass  which  we  have  given  does  not  include 
that  of  the  moon.  The  mass  of  the  latter  is  estimated  at  3x^55  that  of 
the  earth. 

The  masses  of  Jupiter,  Saturn,  Uranus,  and  Neptune  which  we  have 
cited  are  all  derived  from  observations  of  the  satellites  of  these  planets. 
The  masses  derived  from  the  i^erturbations  of  the  planets  do  not  differ 
from  them  by  amounts  exceeding  the  uncertainty  of  the  determinations. 
The  most  noteworthy  deviation  is  in  the  case  of  Saturn,  of  which  Lever- 
rier  has  found  the  mass  to  be  vr^^gTo,  a  result  entirely  incompatible  with 
the  observations  of  the  satellites. 

Diameters. — These  are  also  uncertain  in  many  cases,  especially  in  those 
of  the  outer  planets,  Uranus  and  Neptune.  The  densities  which  we  have 
assigned  to  these  last-mentioned  planets,  depending  on  their  masses  and 
diameters,  must  be  regarded  as  uncertain  by  half  their  entire  amounts. 

Elliptic  Elements. — Of  these  it  may  be  said  that  in  general  they  ai-e  very 
accurate  for  the  planets  nearest  the  sun,  but  diminish  in  j)recision  as  we 
go  outward,  those  of  Neptune  being  doubtful  by  one  or  more  minutes. 

Elements  of  the  Small  Planets. — These  are  only  given  approximately,  in 
order  that  the  reader  may  see  the  relations  of  the  group  at  a  glauce- 
They  are  mostly  taken  from  the  Bei-liner  Astronomisclies  Jahrbuch,  whicc 
gives  annually  the  latest  elements  known.  The  elements  of  the  twenty 
or  thirty  last  ones  are  very  uncertain. 


548 


APPENDIX. 


yn. 


DETERMINATIONS  OF  STELLAR  PARALLAX. 

The  foUo^ing  is  a  list  of  the  stars  the  parallaxes  of  which  are  known 
to  be  investigated,  Avith  the  results  obtained  by  the  different  investiga- 
tors. The  years  are  generally  those  in  which  the  observations  are  sup- 
posed to  have  been  made,  but  in  the  case  of  one  or  two  of  the  earlier 
determinations  they  may  be  those  of  the  publication  of  results.  In  the 
references  the  following  abbreviations  are  used : 

A.  G.  PuiUcationen  der  Astronomischen  Gesellschaft. 
A.N.  Jstrouomische  Xachrkhien. 

B.  M.  Monatshericht  (of  the  Berlin  Academy  of  Sciences). 

C.  R.  Comptes  Eendus  (of  the  French  Academy  of  Sciences). 

D.  O.  Astronomical  Obseiration,  etc.,  at  Dunmnsk,  by  Francis  Briinnow. 

2  Parts.     Dublin,  1870  and  1S74. 
Mel.  Melanges  Mathe'matiques  et  Astronomiqnes,  Academic  de  St.  P^tera- 

bonrg. 
M.  N.  Monthly  Xotices  of  the  Royal  Astronomical  Society. 
M.  R.  A.  S.  Memoirs  of  the  Eoyal  Astronomical  Society. 
M.  P.  Memoires  de  VAcad^mie  de  Sciences  de  St.  Petersbourg. 
P.  M.  Eecueil  des  Memoires  des  Astronomes  de  Poulkoica,  public'  par  W. 

Striire.     St.  Petersbourg,  1853,  vol.  i. 
R.  0.  BadcUffe  Observations,  Oxford. 


Groombridge 

No.  34 

Pote  Star 


Capella . 
Sinus.. . 


AstrODOmer^  &Dd  Date. 


(  Anwers,  by  chronograph  lueasnres,  ) 

1      lS63-'66 J 

Lindenau,  from  R.  A.'s,  1750-1S16 

W.  Struve,  Dorpat,  1S1S-'21 

StraveaudPreass,fromRA.'s,lS22-'3S 
Lnndabl.  from  Dorpat  declinations. . . 

Peters,  from  declinations,  lS42-"-tt 

Lindhagen 

Peters,  from  declinations,  1S42 

'^truve,  with  Palkowa  eqnat.,  1S55  — 
Henderson,  1S33 


0.292 

0.144 
0.075 
0.172 
0.147 
0.067 
0.025 
0.04C 
0.305 
0.34 


Probable 
Error. 


±.036    B.M.,1867. 
p.  65. 


±.030 

±.013 

±.20 

±.043 


P.M. 


P.  M 
P.M. 
P.  M, 
Mel., 
P.M. 


,  p.  121. 
,  p.  264. 
•  p.  136. 
II.,  p.  400. 
.  p.  64. 


DETERMINATIONS  OF  STELLAR  PARALLAX. 


549 


Astronomer,  and  Date. 


Probable 
Error. 


Sirius. 


Castor 

c  Ursffi  Mnj 

Lalaude    No. ) 

211S5 [ 

Lalancle    No. ) 

2125S ) 


Groombridge 

No.  isac 


idge  ) 
'J...f 


Oeltzen    Aig. ) 
N.,No.lT415) 

/3  Ceiilauii 

a  Bootis 

a  Centauri 


p  Ophinchi. 


Maclear,  1S3T 

( Henderson,  from  his  own  and  Mac- ) 

\     leaf's  observations ) 

Gylden,  from  Maclear's  obs.,  1836-'37. 

Abbe,  from  Cape  obs.,  1850-'63 

(Johnson,  with  Oxford  heliometer, '/ 

I     lS54-'55 f 

Peters,  from  declinations,  1842 


Winnecke,  with  heliometer,  1867-'68. . 


Auwers,  1860-'62 

Krueger,  1S62  (?) 

Peters,  from  declinations,  1842 

Paye,  at  the  Paris  Observatory 

( Wichmau,  from  Schliiter's  observa-) 
1     tioiis,  1842-'43 f 

Wichmanu,  from  his  own  obs.,  1851t-| 

Struve,  184T-'49 


Johnson,  with  heliometer,  1854-'56.. . . 

Auwers,  from  Johnson's  obs 

Briiunow,  18T0-'71 


Krueger,  1SC2  (?) 

Moesta,  from  declinations,  lS60-'64  . 
Peters,  from  declinations,  1842 


Johnson,  Oxford  heliometer,  l&45-'55. 

j  Henderson,  from  his  meridian  obs. ) 
(    at  the  Cape  of  Good  Hope,  1832-'33.  [ 
n}  Ceutauri,  from  right  ascensions  . . 
a}  Centauri,  from  direct  declinations. 

ai  Centauri,  from  reflect3d  decs 

cfi  Centauri,  from  right  ascensions  ... 
a^  Centauri,  from  direct  declinations 

a*  Ceutauri,  from  reflected  decs 

Mean  of  all  for  both  stars 

Peters,  from  the  same  ob.s.,  finds 

( Henderson,  from  Maclear's  observa- ) 

'(     tions,  lS39-'40 [ 

Peters,  from  the  same  observations  . . 
Maclear,  from  decs.,  1842-44  and  1S4S. 
Moesta,  from  declinations,  1800-64  . . . 
Krueger,  lS58-'59 


0.16 

0.23 

0.193 
0.2T3 

0.210 

0.133 

0.501 

0.2T1 

0.260 

0.226 

1.08» 

0.180 

0.085 
0.089 
0.034 

0.033 

0.023 
0.09 

0.24T 

0.213 
0.12T 

0.138 


0.92 
1.42 
1.96 
0.48 
1.05 
1.21 
1.16 
1.14 

0.913 

0.970 
0.919 
O.SSO 
0.169 


±.087 
±.102 

±.062 

±.100 

±.011 

±.011 
±.020 
±.141 

±.01S 

±.018 
±.023 
±.029 

±.028 

±.033 
±.01 

±.021 

±.009 
±.073 

±.052 


±.35 
±.19 
±.47 
±.34 
±.18 
±.64 
±.11 
±.11 


±.004 
±.034 
±.068 
±.010 


M.E.A.S.,xi.,248. 

Mel.,  III.,  695. 
M.N.,xxviii.,  p.2. 

R.O.,  xvl.,p.  (xi). 

P.M.,  p.  136. 

A.  G.,  No.  si. 

A.  N.,  No.  1411. 
M.  N.,  xxiii.,  173. 
P.  M.,  p.  136. 

C.  R.,  xxiii. 
A.N.,vol.3C,p.29. 

\lb.,  p.  33. 

P.M.,  p.  291. 
(R.  O.,    xvi.,   p. 
\     (xxii). 

B.  M.,  1874 

D.  O.,  II.,  p.  23. 

M.  N.,  xxiii.,  173. 

A.  N.,  168a 
P.  M.,  p.  13(X 
(R.  O.,    xvi.,   p, 

(     (xxiii). 


M.  R.  A.  &,xi. 
[     p.  67-03. 


; 

p.  M.,  p.  62. 

j  M.  R.  A.  S.,  xiL 

\     p.  370. 

P.M.,  p.  63. 

M.R.A.S.,xx.,98 

A.N.,16S8. 

A.  N.,  1212. 


*  This  result  is  probably  erroneous. 

t  These  results  ofWichmaun  are  parallaxes  relative  to  the  mean  of  certain  stars  of  com- 
parison. He  concluded  that  one  of  the  latter  had  a  large  parallax  which  made  the  paral* 
lax  of  1830  Gr.  0".72 ;  but  this  view  was  afterwards  proved  wrong. 


550 


APPENDIX. 


Star's  Xune. 

p  Ophiuchi . . 
a  Lyrse 


oCygni.. 
eiCygni. 


Astronomer,  and  Dale. 

Knieger,  15^S-'G'2 

Airy,  Tronghton's  circlQ,  1S36 

Airy,  Jones's  circle,  1S36 

Struve,  1537-40 

Peters,  from  declinatious,  1S12 

Struve,  1351-"53 

Johuson,  lS54-"55 

Brunnow,  lS6S-"69 

Bruunow,  1S70 

Peters,  from  declinatioDS,  1S42 

(Bess€l,  with  KOuigsberg  heliome-) 

'(     ter,  1S3S )" 

Bessel,  from  subsequent  obs.,  1S40 

Peters,  from  declinations,  1S42 

(Johnson,  with  Oxford  heliometer, ) 

"(     lS52-'53 ) 

Anwers,  from  Johnson's  obs 

Strove,  l?52-53 

Anwers,  from  Konigsberg  heliometer. 


Par»llai. 

Probable 
Errcr. 

Reference. 

0.162 

±.007 

A.  S.,  1403. 

0.224 

* 

(M.  R  A.  S.,  X., 

-0.102 

)"" 

(     p.  269-270. 

0.262 

P.  M.,  p.  6S. 

0.103 

±.053 

P.  M.,  p.  136. 

0.147 

±.009 

M.P.,viL,vol.i. 

0.154 

±.046 

0.212 

±.010 

D.  0.,  Part  I. 

O.ISS 

±.033 

D.  0.,  Part  n. 

-0.0S2 

±.043 

PM.,p.l3C 

0.314 

0.348 

0.349 

±.0S0 

P.  M.,  p.  136. 

0.392 

R.  0.,  vol.  siv. 

0.42 

0.60C 

±.028 

M.P.,Vn.,  I.,45. 

0.5ft4 

±.016 

A.N.,1411-'16. 

SYNOPSIS  OF  PAPERS  ON  SOLAR  PARALLAX,  1854-78.    551 


VIII. 

SYNOPSIS  OF  PAPERS  ON  THE  SOLAR  PARALLAX,  1854-78. 

The  following  is  believed  to  be  a  nearly  complete  list  of  the  determi- 
nations of  the  solar  parallax  which  have  appeared  since  the  discovery  of 
the  error  of  the  old  parallax  in  1854.  No  papers  have  been  included  ex- 
cept those  which  relate  immediately  to  the  determination  in  question. 

1.  Hansen,  ISbA—M.N.  R.  A.  S.,  xv.,  p.  9. 
Statement  that  he  finds  the  coeflScieut  of  the  parallactic  equation  of  the 
moon  to  be  125".705 — a  value  greater  than  that  deduced  from  the  solar 
parallax  as  given  by  the  transits  of  Venus. 

2.  Leverrier,  1858 — Annales  de  V Observatoire  de  Parts,  iv.,  p.  101. 
Discussion  of  solar  parallax  from  lunar  equation  of  the  earth,  giving 
8".95.     (In  this  paper  Mr.  Stone  has  found  two  small  numerical  errors  -. 
correcting  them,  there  results  8".85.     There  is  also  a  doubt  about  the 
theory,  which  might  allow  the  result  8".78.) 

3.  FoucAULT,  1862 — Comptes  Rendns,  Iv.,  p.  501. 
Experimental  determination  of  the  velocity  of  light,  leading  to  the  value 
of  the  solar  parallax,  8".86. 

4.  Hall,  1863 — Washington  Olservations  for  18G3, -p.  \x. 
Solar  parallax,  deduced  from  observations  of  Mars  with  equatorial  in- 
struments, in  1862 :  result,  8".8415. 

5.  Ferguson,  1863 — Washington  Observations  for  1863,  p.  Ixv. 
Solar  parallax,  deduced  from  observations  with  meridian  instruments  at 
Washington,  Albany,  and  Santiago.     Results  various  and  discordant,  ow- 
ing to  incompleteness  of  the  work. 

6.  Stone,  1863— ilf.  N.  R.  A.  S.,  xxiii.,  p.  183  ;  Mem.  R.  A.  S.,  xxxiii.,  p.  97. 
Discussion  of  fifty-eiglit  con-csponding  observations  of  Mars  (twenty-one 
pairs)  at  Greenwich,  Cape,  and  Williamstown,  leading  to  8".943. 


552  APPENDIX. 

7,  Hajs'SEN,  1863— Jlf.  N.  E.  A.  S.,  xxiii.,  p.  24a 
Deduction  of  the  value  8".97  from  the  parallactic  iuequality  of  the  moon. 

8.  Hansen,  1863— Jlf.  N.  E.  A.  S.,  xxiv.,  p.  8. 
A  more  accurate  computation  from  the  same  data  gives  8".9159. 

9.  WiNNECKE,  1863 — Astr.  Xachr.,  lix.,  col.  261. 
Comparison  of  twenty-six  corresponding  observations  (thirteen  pairs)  atf 
Pulkowa  and  the  Cape  of  Good  Hope.     Parallax,  8".964. 

10.  PowALKY,  1864 — Doctoral  Dissertation,  translated  in  Connaissance  des 

Temps,  1867. 
Discussion  of  the  transit  of  Venus,  1769.     Result,  8".832,  or  8".86  when 
the  longitude  of  Chappe's  station  is  left  arbitrary. 

11.  Stone,  1867— M^.  N.  E.  A.  S.,  xxvii.,  p.  239. 

Attention  directed  to  a  slight  lack  of  precision  in  Hansen's  first  paper 
(Xo.  7).  Deduction  also  from  its  data  of  the  result  8".916 — agreeing  with 
that  from  Hansen's  second  paper. 

12.  Stone,  1867— J/.  N.  E.  A.  S.,  xxvii.,  p.  241. 
Correction  of  one  of  the  numerical  errors  in  Leverrier's  determination, 

Result,  8".91. 

*     13.  Stone,  1867— jlf.  N.  E.  A.  S.,  xxvii.,  p.  271. 
Determination  of  the  parallactic  inequality  of  the  moon  from  2075  ob- 
servations at  Greenwich.     Inequality,  12o".36.     Solar  parallax,  8".85. 

14.  Newcojib,  1867 — Washington  Ohseitations,  186-5,  Appendix  H. 
Discussion  of  the  principal  methods  employed  in  determining  the  solar 
parallax,  and  of  all  the  meridian  observations  of  Mars  during  the  opposi- 
tion of  1862.     Result,  8".848. 

15.  Stone,  1867— Jf.  N.  E.  A.  S.,  xxviii.,  p.  21. 
Comparison  of  Newcomb's  and  Leverrier's  determinations  of  the  solar 

parallax,  leading  to  the  detection  of  another  small  error  in  the  latter. 

16.  Stone,  1868— If.  X.  E.  A.  S.,  xxviii.,  p.  255. 
Rediscussion  of  the  observations  of  the  transit  of  Venus,  1769.     Only 

observations  of  ingress  and  egress  at  the  same  station  are  used,  and  certain 
alterations  are  made  in  the  usual  interpretation  of  the  observations  by 
Chappe  in  California,  and  Captain  Cook  and  his  companions  at  OtaheitA 
The  result  of  these  alterations  is  that  the  parallax  is  increased  to  8".91. 


SYNOPSIS  OF  PAPERS  ON  SOLAR  PARALLAX,  1854-'78.    553 

17.  Newcomb,  1868— M.  N.  R.  A.  S.,  xsix.,  p.  6. 
Criticism  of  Mr.  Stone's  interpretatiou  of  Chappe's  observation  of  egress 
iu  1769. 

18.  Stone,  1868— J/.  N.  R.  A.  S.,  xxix.,  p.  8. 
Reply  to  the  iirecediug  paper. 

19.  Fayk,  1809 — Comptes  Rendus,  Ixviii.,  p.  42. 
Examination   of  tlie  observations   and   interpretations  iu   Mr,  Stone's 

paper,  concluding  that  all  that  we  cau  decide  from  these  observations  is 
that  the  solar  jiarallax  is  between  8".7  and  8".9. 

20.  Stone,  1869— If.  N.  R.  A.  S.,  xxix.,  p.  230. 

Reply  to  Faye,  criticism  of  Powalky's  paper,  and  further  discussions  hav- 
ing for  their  object  to  show  that  the  results  of  liis  paper  agree  with  the 
scattered  observations  of  ingress  and  egress  iu  Europe  and  America. 

21.  Anonymous,  1869 — Vierteljahrssehrift  der  Astr.  Gesel.,  iv.,  p.  190. 
General  review  of  recent  papers  on  the  solar  parallax,  dealing  more 
especially  with  the  work  of  Stone  and  Powalfey. 

22.  POWALKY,  1870  —^sfr.  Nackr.,  Ixxvi.,  col.  161. 

From  a  second  discussion  of  the  transit  of  Venus,  1769,  he  deducee 
8".7869. 

23.  PowALKY,  1871 — Astr.  Nachr.,  Ixxix.,  col.  25. 

From  the  mass  of  the  earth  as  given  by  the  motion  of  the  node  of  Venus, 
8'''.77.  But  the  adopted  mass  of  Venus  enters  into  the  result  in  such  a  way 
as  to  make  it  decidedly  uncertaiu 

24.  Leverrier,  1872^— Comptes  Rcvdits,  Ixxv.,  p.  165. 
Determination  of  the  solar  parallax  from  the  mass  of  the  earth  as  derived 
from  the  motions  of  the  planets,  and  the  diminution  of  the  obliquity  of  the 
ecliptic.  Result,  8''.86.  (The  distinguished  author  of  this  paper  does  not 
distinctly  state  iu  what  way  he  has  allowed  for  the  fact  that  it  is  the  com- 
bined mass  of  the  earth  and  moon  which  is  derived  from  the  perturbations 
of  the  planets,  while  it  is  the  mass  of  the  earth  alone  which  enters  into  the 
formula  for  the  solar  parallax.  His  presentation  of  the  formulae  seems  to 
need  a  slight  correction,  which  will  diminish  the  parallax  to  8".83.) 

25.  CORNU,  1874-'76 — Annales  de  VObsei-ratoirc  de  Paris,  xiii. 
Redetermination  of  the  velocity  of  light,  leading  to  the  parallax  8".794, 
if  Struve's  constant  of  aberration  (20".  445)  is  used. 


554  APPENDIX. 

26.  Galle,  1875 — Breslau,  Marvschke  ^  Berendt. 
"Ueber  eiue  Bestiiumuug  der  Sonueu  Parallaxe  aus  correspondireudeu 
Beobacbtuiigeu  des  Plaueteu  Flora,  iiii  October  nud  Novouiber  1873."    Dis- 
cussion of  observations  made  at  nine  northern  observatories,  and  the  Cape, 
Cordoba,  and  Melbourne,  in  the  southern  hemisphere.     Result,  8".873. 

27.  PuiSEUX,  1875 — Comptes  Rendus,  Ixxx.,  p.  933. 
Computatiou  of  four  contact  observations  of  the  transit  of  Venus  in  1874, 
made  at  Peking  and  St.  Paul's  Island.     Result,  8".879. 

28.  Lindsay  and  Gill,  1877 — M.  N.  R.  A.  S.,  xsxvii.,  p.  308. 
Reduction  of  observations  of  Juno  ^vitli  a  heliometer  at  Mauritius,  in 
1874.     The  result  is  8".765;  or  8".815  when  a  discordant  observation  is 
rejected. 

29.  LI^^)SAY  and  Gill,  1877 — Dunecht  Observatoj'y  Pullications,  ii. 
Observations  and  discussion  from  which  the  preceding  result  is  derived 
given  in  full. 

30.  Airy,  1877  —  Government  Report  on  the  Telescopic  Observations  of  the 

Ti'ansit  of  Vemts. 
Observations  of  contacts  made  by  the  British  expeditions,  and  prelimi- 
nary computation  of  the  results  for  the  solar  parallax.     The  results  given 
on  page  7  are  : 

From  all  the  observations  of  ingress jr=S'''.739    TTf .=10.46 

From  all  the  observations  of  egress 7r=8".S4T    Wt.~.2.5S 

Combined  resnltf jr=S''.760 

31.  Airy,  1877— jlf.  K.  R.  A.  S.,  xxxviii.,  p.  11. 
More  complete  discussion  of  the  British  observations  leading  to  the 
mean  result,  8".754. 

32.  Stone,  1878— Jf.  N.  R.  A.  S.,  xxxviii.,  p.  279. 

Another  discussion  of  the  observations  contained  in  Airy's  report  (No. 

30)  leading  to  the  following  entirely  diflferent  results : 

From  observations  of  ingress Tr=8".S60±0".136Xc 

From  observations  of  egress 7r=S".979-t0".279Xc 

From  all  the  observations 7r=S".8S4  t0".123xe 

33.  Captain  G.  L.  Tupman,  R.  M.  A.—M.  X.  R.  A.  S.,  xxxviii.,  p.  334. 
Statement  that  the  treatment  of  ingress,  as  exhibited  iu  the  Parliament- 
ary Report,  seemed  unsatisfactory.     The  following  are  his  final  results : 

From  observations  of  ingress jr=S".857±0".O4O 

From  observations  of  egress 5r=8".792±0".027 

From  all  the  observations 7r=S".813±0".033 

Note.— In  the  preceding  list  the  abbreviation  M.  X.  R.  A.  S.  represents  the  3[onthly 
Notices  of  the  Royal  Astronomical  Societv  q/  London. 


LIST  OF  ASTRONOMICAL  WORKS.  555 


IX. 

LIST  OF  ASTRONOMICAL  WORKS,  MOST  OF  WHICH  HAVE  BEEN  CON- 
SULTED AS  AUTHORITIES  IN  THE  PREPARATION  OF  THE  PRESENT 
WORK. 

The  following  comprises :  1.  A  few  of  the  leading  works  of  the  great 
astronomers  of  the  past,  and  of  the  investigators  of  the  present,  arranged 
nearly  in  the  order  of  time.  In  the  case  of  works  before  1800,  the  sup- 
posed date  of  composition,  or  the  years  within  which  the  author  flour- 
ished, are  given.  The  list  is  presented  for  the  benefit  of  those  teachers 
and  students  who  wish  to  bo  acquainted  with  these  authorities,  and  can- 
not refer  to  such  works  as  the  BibliograpMe  Astronomique  of  Lalaude,  or 
the  Pulkowa  Catalogns  Lihrorum. 

2.  Modern  telescopic  researches  upon  the  physical  aspects  of  the  planets 
which  have  been  employed  in  the  preparation  of  Part  III.  of  the  present 
work. 

3.  Recent  works  on  special  departments  of  astronomy,  which  may  be 
useful  to  those  who  wish  to  pursue  special  subjects  with  greater  fulness 
than  that  with  which  they  are  treated  in  elementary  works. 

In  the  first  two  classes  the  selection  is,  for  the  most  part,  limited  to 
works  which  have  been  consulted  as  authorities  in  the  preparation  of  this 
treatise.  In  the  case  of  Hevelius,  however,  some  writings  are  added 
which  I  have  not  used,  nor  even  seen,  with  the  object  of  making  the  list 
of  his  larger  works  complete.  Writings  which  have  appeared  in  period- 
icals and  the  transactions  of  learned  societies  are  necessarily  omitted  from 
the  list,  owing  to  their  great  number. 

The  prices  given  for  some  of  the  older  books  are  those  for  which  they 
are  commonly  sold  by  antiquarian  dealers  in  Germany. 

B.C.  250.  Aristarchus  :  De  Magnitudinibus  et  Distantiis  Soils  et  Luna'.  Pisa, 
1572.     $1. 

A.D.  150.  Ptolemy,  Claude  :  mefaahs  2YNTASEQ2  BIBA.  ir,  common- 
ly called  The  Almagest. 

The  most  recent  edition  is  by  the  Abbe  Halma,  in  Greek,  with  French 
transliition.  Two  vols.,  4to.  Paris,  1813-'16.  Commonly  sells  for 
$8  to  §10 


556  APPENDIX. 

880.      Albategnius  :  De  Scientia  Stellarum  Liber.    Bonn,  1645, 

1543l      Copernicus  :  Be  Eevolutionihus  Orbium  Cceleatiuvi. 

The  first  edition  of  tlie  great  work  of  Copernicus  is  rare.  The  second 
(Basel,  1566)  sells  for  $4:.  Two  fine  editions  have  been  published  in 
Germany  in  recent  times.     Price  $7  to  SIO. 

150*.      Tycho    Brake  :     Asfronomice    Instauratce    Mechanica.      Noriberg, 
1602.     $3. 
Contains  description  of  Tycho's  instruments  and  methods  of  observing. 
Astronomioi  Instauratce  Progymnasmata. 

De  Mundi  Mtherei  Becentiorihis  Plmnomenis.  Frank- 
fort, 1610. 

These  two  volumes  generally  go  under  the  title  of  the  former.  A  later 
edition  (1648)  was  issued  under  the  misleading  title  Opera  Omnia.  The 
selling  price  is  $6  for  the  two. 

1596-  )  Kepler,  Johannes  :    Opera  Omnia.      Edidit  Dr.  Ch.  Friscli.      8 

1630.  >      vols.,  8vo.     Frankfort,  1858-71. 

A  recent  and  complete  edition  of  Kepler's  voluminous  writings.  Price 
from  $35  to  $oO.    Generally  cheaper  at  second-hand. 

1590-  )  Galileo  Galilei  :    Ope^-e.      13  vols.,  8vo.      Milan,  1811.      Price 

1636.  \      about  $10. 

A  much  better  edition,  published  in  4to,  about  1845,  is  more  expensive. 
Galileo  wrote  almost  entirely  in  Italian. 

1603.      Bayer,  Johannes  :   Uranometria. 

Bayer's  celebrated  star-charts,  in  which  the  stars  were  first  named  with 
Greek  letters.  Three  or  more  editions  were  published,  the  second  be- 
ing in  1648,  the  third  in  1661.     $2  50. 

RicciOLUS :  Almagestum  Novum.    2  vols,  in  one,  folio.     Bonn,  1651. 

Astronomia  Beformata.     Folio.     Bonn,  1665. 

Two  ambitious  works,  remarkable  rather  for  their  voluminousness  than 
for  their  value.  The  author  being  an  ecclesiastic,  had  to  profess  a  dis- 
belief in  tlie  Copcrnican  system. 

1630.      BuLLiALDUS :  Astronomia  Philolaica.     Folio.    Paris,  1645. 

The  last  three  works  arc  cited  as  probably  the  most  voluminous  com- 
pendiums  of  astronomy  of  the  seventeenth  century.  They  can  all  btJ 
purchased  for  $3  or  $4  each. 

1611.      Fabritii,  J. :  De  Maculis  in  Sole  Observatis. 

1655.      Borelli  :  De  Fero  Telescopii  Inventore.     Hague,  1655.    $1. 

1647-  } 

_      >  Hevelius,  J. :  Selenograpliia,  sive  LuncB  Descriptio.     Folio. 

The  earliest  great  work  on  the  geography  of  the  moon  and  the  aspects 
of  the  planets.    Profusely  illustrated.    §4  to  §5. 


LIST  OF  ASTRONOMICAL  WORKS.  557 

Hevelius,  J. :  Mereurius  in  Sole  Visus.     Folio,  1662.     $1. 

Contains  also  Horrox's  observation  of  the  transit  of  Venus  in  1639. 

CometograpMa.     Folio,  1668. 

The  first  great  modern  treatise  on  the  subject  of  comets. 

Machina  Coelestis,  Pars  Prior.     Folio,  1G73. 

Contains  descriptions  of  his  instruments,  and  a  disquisition  on  tlie  prac- 
tical astronomy  of  his  time.  * 

Machina  Coelestis,  Pars  Posterior.     Folio,  1679. 

A  very  rare  book,  almost  the  entire  edition  having  been  destroyed  by 
fire.     A  copy  was  sold  for  $50  in  1873. 

Annus  Climactericus.     Dautzic,  1685. 

Prodromus  Astronomice.     Dantzic,  1690. 

Firmamentum  Sohiescianum.     Dantzic,  1690. 

These  works  comprise  star-catalogues,  star-maps,  etc.    $3  50. 

1653       HuYGHENS :  Systema  Saturnium.     Hague,  1659. 

Horologium  Osdllatorium.     Paris,  1673. 

The  latter  work  contains  the  theory  of  the  pendulum  clock.  These  two 
and  most  of  the  other  important  works  of  Iluyghens  were  published 
in  Leiden  in  1751,  under  the  title  of  Opera  Mtchajiica,  Geometrka,  As- 
tronomica  et  Miscellanea,  nominally  in  four  volumes,  but  the  paging  is 
continuous  throughout  the  series,  the  total  number  of  pages  being 
776.    Leiden,  1751.     $5. 

1687.      Newton,  Isaac  :  Philosophice  Naturalis  Principia  Mathematica.    4to. 

London,  1687. 

A  number  of  editions  of  Newton's  Principia  have  appeared.  One  of  the 
most  common  is  that  of  Le  Scur  and  Jacquicr,  3  vols,  in  4.  Geneva, 
1731).  It  is  accompanied  by  an  extended  commentary.  Sells  for  about 
$4.  A  very  fine  edition  was  issued  in  1871,  by  Sir  William  Thomson,  in 
Glasgow.  There  is  also  an  English  translation  by  Motte,  which  has 
gone  through  several  editions  in  England  and  one  in  America. 

Brewster,  Sir  D.  :  Memoirs  of  tlie  Life,  Writings,  and  Discoveries 
of  Sir  Isaac  Newton.     2  vols.,  8vo.     Edinburgh,  1855. 

1720.      Flamsteed,  J. :  Ristoria  Coelestis  Briiannica.     3  vols.,  folio.    Lou- 
don, 172.5.     $10. 
Contains  Flamsteed' s  observations  and  star-catalogue. 

1728.      Blanchini,  F.  :  Hesperi  et  Phosphori  nova  Phwnomena  sive  Observa- 
.  Hones  circa  Planetam  Veneris.     Folio.     Rome,  1728. 

1740.  Cassini  :  j^lemens  d^ Astronomic.     4to.     Paris,  1740.     $1. 

1741.  Weidler,  Jo.  :    Historia  Astronomice.      Small  4to.      Wittemberg, 

1741.    $2. 

Bernouxlli,  John  :    Opera  Omnia.     4  vols.,  4to.    Lausanne,  1742. 


558  APPENDIX. 

Le  Monnier  :  La  Th4orie  des  ComHes.     1  vol.,  8vo.     Paris,  1743, 
$1. 
1760.      Kant,   Immanuel  :    Schriften    zur    PhysiscJien    Geof/ra])hie.      8vft 
Lei^izig,  1839. 

1780,     PiNGRE :    Com^tographie ;   ou  Traite  Historique  et  Theorique  des  Co- 
metes.     2  vols.,  4to,     Paris,  1783. 

The  most  complete  Listorical  and  general  treatise  on  comets  which  has 
appeared. 

1780-  )  Bailly  :  Histoirc  de  VAstronomie  Ancienne  dejmis  son  OrUjine  jusqu'd, 
1790.  S      V£:tailissemcntdeV£coled'Alexaudrie.    lvol.,4to.   Paris,  1781.  $10. 

Histoire  de  VAstronomie  Moderne  dejyuis  la  Fondation  de 

V£cole  d'Alexandrie,ju8qu'a  VJipoque  de  MDCCXXX.     3  vols.,  4to. 
Paris,  1779.     $6. 

Traits  de  VAstronomie  Indienne  et  Orientale.     1  vol.,  4to. 


Paris,  1787. 

These  histories  by  Bailly  are  considered  very  unsound,  the  author  hav- 
ing a  greatly  exaggerated  opinion  of  the  knowledge  of  the  ancients. 

1800.      Lalakde,  J.  De  :    BiUiograpMe  Astronomique ;    avec  V Histoire  de 
VAstronomie  depuis  1781  jttsqu'd,  1802.     4to.     Paris,  1803.     $3. 

1817.      Laplace,  P.  S. :   Traite  de  M4canique  Celeste.     4  vols.,  4to.     Paris, 

1799-1805.    $60. 

This  work  is  now  expensive,  all  the  editions  being  exhausted.    A  new 
edition  is  soon  to  be  issued. 

Exposition  dii  Systhie  du  Monde.     1  vol.,  4to.    $2. 

The  latter  work  gives  a  very  clear  popular  exposition  of  the  laws  of  the 
celestial  motions. 

Delambre:  Histoire  de  VAstronomie  Ancienne.     2  vols.,  4to.     Paris, 
1817.     |4. 

Histoire  de  VAstronomie  du  Moyen  Age.    1  vol.,  4 to.     Paris, 


1819,     $3, 
Histoire  de  VAstronomie  Moderne.     2  vols.,  4to,     Paris, 


1821.     $5. 

Histoire  de  VAstivnomie  au  dix  -  liuitieme  Siecle.     1  vol,,  4to.     Paris, 

1827.     $3. 

These  histories  by  Delambre  consist  principally  of  abstracts  of  the  writ- 
ings of  all  eminent  astronomers,  accompanied  by  a  running  commen- 
tary, but  without  any  attempt  at  logical  arrangement.  Each  work  is 
taken  up  and  passed  tlirough  in  regular  order,  but  it  is  only  in  the  in- 
troductory essays  that  general  views  of  the  progress  of  the  science  are 
founJ. 


LIST  OF  ASTRONOMICAL   WORKS.  559 

Encke,  J.  F.  :  Die  Enifernung  der  Sonne  von  der  Erde  mis  dem  Ve- 
nusdurchgange  von  1761  hergeleitet.     12mo.     Gotba,  1822. 

Der  Venusdurchgang  von  1769.     12iiio.     Gotha,  1824. 

These  two  little  books  contain  Encke's  researches  on  the  solar  parallax 
leading  to  the  result  8".5776,  and  the  distance  of  the  sun  95,300,000 
miles. 

IDELER,  Dr.  Ludwig  :  Randhmli  der  Mathematischen  und  Techniachm 
Chronologie.     2  vols.,  8vo.     Berlin,  1825. 

An  exhaustive  and  commendable  work  on  the  measures  of  time  adopted 
in  various  countries,  especially  in  ancient  times. 

Whewell,  Wm.  :  History  of  the  Inductive  Sciences.     London. 

Herschel,  Sir  John  :  Results  of  Astronomical  Observations  made 
during  the  Years  1834,  '5,  '6,  '7,  '8,  at  the  Cape  of  Good  Hope.  1 
vol.,  4to.     London,  1847. 

Struve,  F.  G.  W.  :  £tudes  d'Astronomie  Stellaire.      St.  Petersburg, 

1847. 

Grant,  Robert  :  History  of  Physical  Astronomy,  from  the  Earliest 
Ages  to  the  Middle  of  the  Nineteenth  Century.     8vo.     London,  1852. 

BiOT,  J.  B. :  Etudes  sur  V Astronomic  Indienne  et  Chinoise.  8vo. 
Paris,  1862. 

LovERiNG,  Joseph  :  On  the  Periodicity  of  the  Aurora.  Memoirs 
of  the  American  Academy  of  Arts  and  Sciences.  Boston,  1859 
and  1865. 

Olbers,  W.,  and  Galle,  J.  G. :  Die  leichtste  und  hequemste  Methode 

die  Bahn  eines  Cometen  zu  herechnen.     8vo.     Leipzig,  1864. 

This  work  contains  a  table  of  all  orbits  of  comets  computed,  broueht  up 
to  the  end  of  1863. 

IZoLLNER,  Dr.  J.  C.  F. :  Ueher  die  Natur  der  Kometen.    8vo.     Leipzig, 

1872. 

DtJHRiNG,  Dr.  E.  :  Kritische  Geschichte  der  Princi2)ien  der  Mechanik. 
8vo.     Berlin,  1873. 

ToDHUNTER,  I. :  History  of  the  Mathematical  Theories  of  Attraction 
and  the  Figure  of  the  Earth,  from  the  Time  of  Newton  to  that  of  La 
Place.     2  vols.,  8vo.     London,  1873. 

n.— WORKS  ON  THE  PHYSICAL  ASPECTS  OP  THE  PLANETS. 
SCHROETER,  J.  H.  :   BeitrUge  zu  den  Neuesten  Astronomischen  Ent- 

deehungen.    Herausgegeben  von  Bode.     3  vols.,  8vo.    Berlin,  1786- 

1800.     $5. 

Bj5  37 


560  APPENDIX. 

SCHROETER,  J.  H.  :  SelenotopograpMscJie  Fragmente  zur  genauei'n 
Kenntniss  dcr  Mondfldche.     4to.     Lilientbal,  1791.     $3. 

Jphroditographische  Fragmente  zur  genauern  Ketmtniss  des 

Planeten  Venus.     4to.     Helmstedt,  1796.     $(5. 

Schroeter's  style  was  intolerably  prolix  and  diflfuse,  so  that  a  clear  idea 
of  the  results  he  really  attained  involves  no  small  labor. 

Beer,  W.,  and  Madler,  J.  H. :  Physische  Beobaclitungen  des  Mars 
bei  seiner  Opposition  im  September  1830.     12mo.     Berlin,  1830. 

Der  Mond  nach  seinen  liosmischen  und  individuellen  Vcr- 

hdltnisscn,oder  Allgcmeine  vergleichende  SelenograpMe.   4to.   Berlin, 

1837.     §7. 

This  volume  is  accompanied  by  a  large  map  of  the  moon,  and  is  the 
most  complete  and  celebrated  work  on  selenography  wliich  has  yet 
appeared. 

Beer,  W.,  and  Madler,  J.  H. :  Beitrdge  zur  physischen  Kenntniss 
der  himmlischen  Korper  im  Sonnensysteme.     4to.     Weimar,  1841. 

ZoLLNER :  Photometrische  Untersuchungen  mit  besonderer  Eiicksicht 
auf  die  pliysische  Beschaffenheit  der  Himmelskorper.  8vo.  Leip- 
zig, 1865. 

Engelsiaxn^  :  Ueber  die  HelligkeitsverTialtnisse  der  JupitersirdbanteS, 
8vo.     Leipzig,  1871. 

VoGEL,  H.  C,  and  Lohse  :  Beobaclitungen  angestellt  auf  der  Sterti' 
u-arte  des  Kammerlierrn  von  Biilow  zu  Botlikamp.  3  pts.,  4to.  Leip- 
zig, 1872-75. 

III.— RECENT  TREATISES  ON  SPECIAL  SUBJECTS. 

The  Sun. 

Proctor,  E.  A. :  The  Sun  :  Puler,  Fire,  Light,  and  Life  of  the  Plan- 
etary System.    Bvo.     London,  1871. 

LocKYER,  J.  N. :  Contnbutions  to  Solar  Physics.    8vo,  London,  1874. 

Secchi,A.  :  Le  Soldi.     2  vols.,  8vo, -with  Atlas.     Paris,  1875-77. 

The  latter  is  the  most  complete  and  beautifully  illustrated  treatise  on 
the  sun  which  has  yet  appeared. 

The  Moon. 
Nasmtth  and  Carpenter  :  The  Moon.     London,  1874. 
Contains  very  beautiful  illustrations  of  lunar  sceneiy. 
Proctor,  E.  A. :    Tlie  Moon :   Her  Motions,  Aspects,  Scenery,  and 

Physical  Condition.     8vo.     London,  1873. 
This  work  is  illustrated  with  several  of  Mr.  Rutherfurd's  photographs. 


LIST  OF  ASTBOKOMICAL  WORKS.  561 

Neison,  Edmund  :  The  Moon,  and  the  Condition  and  Configurations 

of  its  Surface.     Illustrated.     8vo.     London,  1876. 
Pi-iucijjally  devoted  to  selenography. 

Trajtsits  of  Vexus. 

Forbes,  George  :  Transits  of  Venus.    London,  1874. 

Proctor,  K.  A. :   Transits  of  Venus.     A  Popular  Account  of  Past 
and  Coming  Transits.     8vo.     Loudon,  1875. 


THEORETICAL  AND   PRACTICAL  ASTRONOMY. 

LoOMis,  Elias  :  An  Introduction  to  Practical  Astronomy,  with  a  CoU 

lection  of  Astronomical  Tables.     8vo.     New  York,  1855. 
Contains  much  information  for  the  amateur  astronomer. 

Sa WITCH :  Airiss  der  Practischen  Astronomic.     2  vols.,  8vo.     Ham- 
burg, 1850. 

Brunxow,  F.  :  Practical  and  Spherical  Astronomy.     8vo.     London 
and  New  York,  1865. 

Chauvenet,  W.  :  Manual  of  Spherical  and  Practical  Astronomy.    2 
vols.,  8vo.     Philadelphia,  1863. 

The  most  complete  and  exhaustive  treatise  on  the  subject  which  has  yet 
appeared. 

Watson,  J.  C. :  Theoretical  Astronomy.     8vo.     Philadelphia,  1868. 


562  APPENDIX. 


X. 

GLOSSARY  OF  TECHNICAL  TERMS  OF  FREQUENT  OCCURRENCE  IN 
ASTRONOMICAL  WORKS. 

The  following  list  is  believed  to  include  all  the  technical  terms  used  in 
the  present  work,  as  well  us  a  number  of  others  which  the  reader  of  as- 
tronomical literature  will  frequently  meet  with.  The  words  in  parenthe- 
ses which  sometimes  follow  a  term  express  its  literal  signification. 

Aberration  (a  tmridering-aivay).  Generally  applied  to  a  real  or  apparent 
deviation  of  the  course  of  a  ray  of  light.  Especially  (1)  an  apparent 
displaccuieut  of  a  star,  owing  to  the  progressive  motion  of  light  com- 
bined with  that  of  the  earth  in  its  orbit,  p.  209 ;  (2)  the  defects  of  action  of 
a  lens  in  not  bringing  all  rays  to  the  same  focus.  The  spherical  aberration 
->f  a  lens  results  in  the  rays  which  pass  through  the  glass  near  its  edge 
ooaiing  to  a  shorter  focus  than  those  which  pass  near  its  centre,  while 
the  chroynatic  aberration  is  the  separation  of  the  light  of  different  colors. 
Achromatic  {without  color).    Applied  to  an  object-glass  in  which  rays  of 

diifereut  colors  are  brought  to  the  same  focus.     See  p.  116. 
Aerolite.    A  meteoric  stone  or  other  body  falling  from  the  celestial  spaces- 
Albedo.    Degree  of  whiteness,  or  proportion  of  incident  light  reflected  by 
a  non-luminous  body.     When  the  albedo  of  a  body  is  said  to  be  0.6,  it 
means  that  it  reflects  -j^  of  the  incident  light. 
Alidade.    A  movable  frame  carrying  the  microscopes  or  verniers  of  a  grad- 
uated circle.     Not  generally  used  in  instruments  of  recent  construction. 
Altitude.     The  apparent  angular  elevation  of  a  body  above  the  horizon, 
usually  expressed  in  degrees  and  minutes.     At  the  horizon  the  altitude 
is  zero,  at  the  zenith  it  is  90°. 
Annular  (ring-shajied).     Having  the  appearance  or  form  of  a  ring. 
Anomaly.     The  angular  distance  of  a  planet  from  that  point  of  its  orbit 
in  which  it  is  nearest  to  the  sun,  or,  in  the  ancient  astronomy,  to  the 
eartli.     Draw  two  straight  lines  from  the  sun,  one  to  the  nearest  point 
of  tiie  orbit,  or  the  perihelion,  and  the  other  to  the  planet,  and  the  an- 
gle between  these  lines  will  be  the  anomaly  of  the  planet. 
Anomalistic.     Pertaining  to  the  anomaly.     The  anomalistic  year  is  the 
period  between  two  consecutive  returns  of  the  earth  to  its  perihelion. 
It  is  about  4'  15"  longer  than  the  sidereal  year. 


GLOSSABY  OF  TECHNICAL   TEEMS.  563 

Ansae  (handles).  The  apparent  ends  of  the  rings  of  Saturn,  which  look 
like  handles  projecting  from  the  planet. 

Aperture  of  a  Telescope.  The  diameter  of  the  glass  or  mirror  which 
admits  the  rays  of  light,  clear  of  all  obstacles. 

ApheHon.  The  part  of  the  orbit  of  a  planet  in  which  it  is  farthest  from 
the  sun. 

Apogee.  The  point  of  an  orbit  in  which  the  planet  is  farthest  from  the 
earth.  In  the  ancient  astronomy  the  planets  were  said  to  be  in  apogee 
when  beyond  the  sun,  and  therefore  at  their  greatest  distauce  from  the 
earth;  but  the  term  is  now  applied  only  to  the  most  distant  point  of 
the  moon's  orbit. 

Apsis  (pi.  Apsides).  The  two  points  of  an  orbit  which  are  nearest  to,  aud 
farthest  from,  the  centre  of  motion,  called,  respectively,  the  lower  arid 
higher  apsis.  The  line  of  apsides  is  that  which  joins  these  two  points, 
and  so  forms  the  major  axis  of  an  elliptic  orbit.  The  term  is  now  near- 
ly superseded  by  the  more  special  terms  aphelion,  perilielion,  perixjee,  ^ic. 
See  Elements. 

Anjaillary  Sphere.  A  combination  of  circles  used  before  the  invention  of 
the  telescope  for  determining  the  relative  directions  or  apparent  posi- 
tions of  the  heavenly  bodies  on  the  celestial  sphere.  It  is  now  entirely 
out  of  use.     See  p.  107. 

Astrolabe.  A  simple  form  of  armillary  sphere  used  by  the  auciout  as- 
tronomers. 

Azimuth.  The  angular  distance  of  a  point  of  the  horizon  from  the  north 
or  south.  The  azimuth  of  a  horizontal  line  is  its  deviation  from  the 
true  north  and  south  direction.  The  azimuth  of  the  east  and  west 
points  is  90°. 

Binary  System.  A  double  star,  in  which  the  two  components  are  found 
to  revolve  round  each  other. 

Binocular  (two-eyed).  Applied  to  a  telescope  or  microscope  iu  which  both 
eyes  can  be  used  at  once,  as  an  opera-glass. 

Black  Drop.  A  distortion  of  Mercury  or  Venus  at  the  time  of  internal 
contact  with  the  limb  of  the  sun.     See  p.  179. 

Centesimal.  Eeckoning  by  hundreds.  Applied  to  those  denominational 
systems  in  which  each  unit  is  one  hundred  times  that  next  below  it. 
The  centesimal  division  of  the  angle  is  one  in  which  the  quadrant  ia 
divided  into  100  degrees  or  grades,  the  grade  into  100  minutes,  and  the 

,     minute  into  100  seconds. 

'Chronograph  (time-mark).  An  instrument  for  measuring  time  by  mark- 
ing on  a  moving  paper  (see  p.  157J.  Time  is  then  represented  by 
space  passed  over. 

Circle,  Great.  A  circle  which  divides  the  sphere  into  two  equal  hemi- 
spheres, as  the  equator  and  the  ecliptic. 


564  APPENDIX. 

Colurea  Tho  four  principal  meridians  of  the  celestial  sphere,  aU  of  which 
pass  from  the  pole,  and  one  of  which  passes  through  each  equinox,  and 
one  through  each  solstice.  They  mark  the  circles  of  0^,  C",  12'',  and  IS' 
of  right  ascension,  respectively. 

Conjunction  (a  joining).  The  nearest  apparent  approach  of  two  heavenly 
hodies  which  seem  to  pass  each  other  in  their  course.  They  are  com- 
monly considered  as  in  conjunction  when  they  have  the  same  longitude. 
The  term  is  applied  especially  iu  the  case  of  a  planet  and  the  sun.  The 
nearest  approach  is  called  superior  conjunction  when  the  planet  is  he- 
yond  the  sun,  inferior  when  it  is  this  side  of  it.  Mercury  and  Venus 
are,  of  course,  the  only  planets  which  can  he  in  inferior  conjunction. 

Cosmical.  Eelating  to  creation  at  large,  in  contradistinction  to  terres- 
trial, which  relates  to  the  earth.  By  a  cosmical  phenomenon  is  meant 
one  which  has  its  origin  outside  the  earth  and  its  atmosphere. 

Culmination.  The  passage  of  a  heavenly  body  over  the  meridian  of  a 
place.  This  passage  may  be  considered  as  occurring  twice  in  a  day, 
once  above  the  pole,  and  again  below  it,  twelve  hours  later.  The  for- 
mer is  called  the  upper,  the  latter  the  lower,  culmination.  Tho  upper 
culmination  of  the  sun  occurs  at  noon,  the  lower  at  midnight. 

Cusps  {points).  The  pointed  ends  of  the  seeming  horns  of  the  moon  or 
of  a  planet  when  it  presents  the  appearance  of  a  crescent. 

Cycle  (circle).  A  period  of  time  at  the  end  of  which  any  aspect  or  rela- 
tion of  the  heavenly  bodies  recurs,  as  the  Metouic  cycle. 

Declination.  The  angular  distance  of  a  heavenly  body  from  the  equator. 
When  north  of  the  equator,  it  is  said  to  be  in  north  declination ;  other- 
wise, iu  south  declination. 

Deferent.  In  the  ancient  astronomy  the  mean  orbit  of  a  planet  which 
was  supposed  to  carry  the  epicycle.  It  is  represented  by  the  dotted 
circles  in  Figs.  10  and  11,  pp.  38  and  39. 

Dichotomy  (a  cutting  in  two).  The  aspect  of  a  planet  when  half  illumi. 
nated,  as  the  moon  at  first  and  last  quarter. 

Digit.  The  twelfth  part  of  the  diameter  of  the  sun  or  moon,  formerly 
used  to  express  the  magnitude  of  eclipses.     See  p.  28. 

Dip  of  the  Horizon.  At  sea,  the  depression  of  the  apparent  horizon  be- 
low the  true  level,  owing  to  the  height  of  the  observer's  eye  above  the 
water. 

Direct  Motion.  A  motion  from  west  to  east  among  the  stars,  like  that 
of  tho  planets  in  general. 

Eccentric.  In  the  ancient  astronomy,  a  circle  of  which  the  centre  was 
displaced  from  the  centre  of  motion.     See  p.  42,  Fig.  13. 

Eccentricity.     See  Elements. 

Ecliptic.  The  apparent  path  of  the  sun  among  the  stars,  described  in 
Part  I.,  Chap.  I.,  §  3.     See  p.  13. 


GLOSSARY  OF  TECHNICAL  TEEMS.  565 

Egress  (a  going  forth).  The  end  of  the  apparent  transit  of  one  body  over 
another,  when  the  former  seems  to  leave  the  latter. 

Elements.  In  general,  the  data  for  predicting  an  astronomical  phenome- 
non. EspeciaUy,  the  quantities  which  determine  the  motion  of  a  plan- 
etary body.  The  independent  elements  of  a  planet  are  six  in  number, 
namely : 

1.  The  mean  distance,  or  half  the  longer  axis,  AP,  of  the  ellipse  in  which 
the  planet  moves  round  the  sun,  the  latter  being  in  the  focus  at  S. 

2.  The  eccentricity,  the  ratio  of  the  distance  CS  between  the  centre 
and  focus  of  the  ellipse  to  the  mean  distance. 

These  two  elements  determine  the  size  and  form  of  the  elliptic  orbit 
of  the  planet. 


Fig.  112.— Diagram  illustratiug  elliptic  elements  of  a  planet 

3.  The  longitude  of  the  ascending  node,  which  gives  the  direction  of 
the  line  in  which  the  plane  of  the  orbit  intersects  that  of  the  ecliptic,  or 
the  angle  which  this  line  makes  with  the  vernal  equinox. 

4.  The  inclination  of  the  plane  of  the  orbit  to  that  of  the  ecliptic. 

5.  The  longitude  of  the  perihelion,  P,  for  which  is  taken  the  longitude 
of  the  node,  plus  the  angular  distance  from  the  node  to  the  perihelion, 
as  seen  from  the  sun. 

These  three  quantities  determine  the  position  of  the  orbit  in  space. 

6.  The  mean  longitude  of  the  planet  at  some  given  epoch,  or  the  time 
at  which  it  passed  the  perihelion,  P. 

To  these  six  the  time  of  revolution,  or  mean  angular  motion  in  a  day 
or  year,  is  usually  added ;  but  as  this  can  always  be  determined  from 
the  mean  distance,  and  vice  versa,  by  Kepler's  third  law,  the  two  are  not 
regarded  as  independent  elements. 

The  quantities  we  have  described  are  usually  represented  by  algebraio 
symbols,  as  follows : 

a,  the  mean  distance.  w  or  n,  the  longitude  of  the  perihelion. 

e,  the  eccentricity.  e,  the  mean  loni^itude  at  some  epoch. 

6  or  n,  the  longitude  of  the  node.  n,  the  mean  motion. 

i  or  <p,  the  inclination.  w,  the  distance  from  node  to  perihelion. 


566  APPENDIX. 

Ellipticity.  Deviation  from  a  truly  circnlar  or  spherical  form,  so  as  to 
become  an  ellipse  or  spheroid.  An  orbit  is  said  to  be  more  elliptic  the 
more  it  deviates  from  a  circle. 

Elongation.  The  apparent  angular  distance  of  a  body  from  its  centre  of 
motion,  as  of  Mercury  or  Venus  from  the  sun,  or  of  a  satellite  from  its 
primary. 

Emersion  (a  coming  out).  The  reappearance  of  an  object  after  being 
eclipsed  or  otherwise  hidden  from  view. 

Ephemeris.  A  table  giving  the  position  of  a  heavenly  body  from  day  to 
day,  in  order  that  observers  may  know  where  to  look  for  it.  Api)lied 
also  to  an  astronomical  almanac  giving  a  collection  of  such  tables. 

Epicycle.  In  the  ancient  astronomy,  a  small  circle  the  centre  of  which 
moves  round  on  the  circumference  of  a  larger  one,  especially  the  circle 
in  which  the  three  outer  planets  seemed  to  perform  an  annual  revolu- 
tion in  consequence  of  the  revolution  of  the  earth  around  the  sun. 

Equation  of  the  Centre.  The  angular  distance  by  which  a  planet  mov- 
ing iu  an  ellipse  is  ahead  of  or  behind  the  mean  position  which  it 
would  occupy  if  it  moved  uniformly.  It  arises  from  the  eccentricity  of 
the  ellipse,  vanishes  at  perihelion  and  aphelion,  and  attains  its  greatest 
value  nearly  half-way  between  those  points. 

Equation  of  Time.     See  p.  166. 

Equator.  The  great  circle  half-way  between  the  two  poles  in  the  earth 
or  heavens.  The  celestial  equator  is  the  line  EF  in  Fig.  3,  p.  12.  See 
also  pp.  62,  and  148,  ]  49. 

EquatoreaL  A  telescope  mounted  so  as  to  follow  a  star  in  its  apparent 
diurnal  course,  as  described  on  p.  119. 

Equinox.  Either  of  the  two  points  iu  which  the  sun,  in  its  apparent  an- 
nual course  among  the  stars,  crosses  the  equator.  So  called  because  the 
days  and  nights  are,  when  the  sun  is  at  those  points,  equal. 

Evection.  An  inequality  in  virtue  of  which  the  moou  oscillates  about 
IJ^  on  each  side  of  her  meau  position  iu  a  period  of  31  days  19  hours. 

Eye-piece,  of  a  telescope.  The  small  glasses  nearest  to  the  eye,  which 
magnify  the  image.     See  pp.  112  and  120. 

Faculae  (small  torches).  Groups  of  small  shining  spots  on  the  surface  of 
the  sun  which  are  brighter  than  other  parts  of  the  photosphere.  Tliey 
are  generally  seen  in  the  neighborhood  of  the  dark  spots,  and  are  sup- 
posed to  be  elevated  portions  of  the  photosphere. 

Filar  {made  of  thread).     Applied  to  micrometers  made  of  spider  lines. 

Focus  (a  fireplace).  A  point  in  which  converging  rays  all  meet.  The 
focus  of  a  telescope  is  the  point  at  which  the  image  is  formed.    See  p.  11 L 

Geocentric.  Referred  to  the  centre  of  the  earth.  The  geocentric  posi- 
tion of  a  heavenly  body  is  its  position  as  seen  or  measured  from  the 
earth's  centre. 


GLOSSARY  OF  TECHNICAL  TERMS.  567 

Geodesy.  The  art  or  science  of  measariug  the  earth  without  reference 
to  the  heavenly  bodies. 

Gnomon.  In  the  old  astronomy,  the  style  of  a  sundial  or  any  object  the 
sliadovr  of  which  is  measured  in  order  to  learn  the  position  of  the  sun. 

Golden  Number.  The  number  of  the  year  in  the  Metonic  cycle,  counted 
from  1  to  19.     See  p.  48. 

Heliacal  {relating  to  the  sun).  Applied  iu  the  ancient  astronomy  to  those 
risings  or  settings  of  bright  stars  which  took  place  as  near  to  sunrise 
or  sunset  as  they  could  be  observed. 

Heliocentric.  Referred  to  the  sun  as  a  centre.  Applied  to  the  positions 
of  the  heavenly  bodies  as  seen  from  the  suu's  centre. 

Heliometer.  An  instrument  in  which  the  object-glass  is  sawed  into  two 
equal  parts,  each  of  the  parts  forming  au  independent  imago  of  a  heav- 
enly body  iu  the  focus.  When  the  two  parts  are  together  in  their  origi- 
nal position,  these  images  coincide,  but  by  sliding  one  part  on  the  other 
they  may  be  separated  as  far  as  is  desired  for  the  purposes  of  measure- 
ment. It  is  much  used  in  Germany  for  measuring  distances  too  great 
for  the  application  of  a  filar  micrometer. 

Heliostat.  Au  instrument  iu  which  a  mirror  is  moved  by  clock-work  in 
such  a  way  as  to  reflect  the  rays  of  the  sun  in  a  fixed  direction,  notwith- 
standing the  diurnal  motion. 

Heliotrope.  An  instrument  invented  by  Gauss  for  throwing  a  ray  of  sun- 
light iu  the  direction  of  a  distant  station.  It  is  much  used  in  geodetic 
measurements. 

Hour  Angle.  The  distance  of  a  heavenly  body  from  the  meridian,  meas- 
ured by  the  angle  at  the  pole.  It  is  commonly  expressed  in  time  by  the 
number  of  hours,  minutes,  etc.,  since  the  body  crossed  the  meridiau. 

Immersion  {aplunginrj  in).  The  disappearance  of  a  body  iu  the  shadow 
of  another,  or  behind  it. 

Inclination,  of  an  orbit.     See  Elements. 

Ingress  (a  going  iti).  The  commencement  of  the  transit  of  one  body  ovei 
the  face  of  another. 

Latitude.  The  angular  distance  of  a  heavenly  body  from  the  ecliptic,  as 
declination  is  distance  from  the  equator. 

Libration  (a  sloiv  sicinging,  as  of  a  lalance).  The  seeming  slight  oscillations 
of  the  moon  around  her  axis,  by  which  we  sometimes  see  a  little  on  one 
side  of  her,  and  sometimes  on  the  other. 

Longitude.  If  a  perpendicular  be  dropped  from  a  body  to  the  ecliptic,  its 
celestial  longitude  is  the  distance  of  the  foot  of  the  perpendicular  from 
the  vernal  equiuox  counted  towards  the  east. 

Lunation.  The  period  from  one  change  of  the  moon  to  the  next.  Its 
duration  is  2^\  days,  or,  more  exactly,  29.5305879  days. 

Mass,  of  a  body.     The  quantity  of  matter  contained  iu  it,  as  measured 


568  APPENDIX. 

by  its  weight  afc  a  given  place.  Mass  differs  from  weight  in  that  the 
latter  is  different  in  different  places  even  for  the  same  body,  depending 
on  the  intensity  of  gravity,  whereas  the  mass  of  a  body  is  necessarily  the 
same  everywhere. 

Mean  Distance.     See  Elements. 

Meridian.  The  terrestrial  meridian  of  a  place  is  the  north  and  sonth 
vertical  plane  passing  through  that  place,  or,  the  great  circle  in  which 
this  -plane  intersects  the  celestial  sphere.  It  passes  through  the  pole, 
the  zenith,  and  the  north  and  south  points  of  the  horizon.  Celestial 
meridians  are  great  circles  passing  from  one  pole  of  the  heavens  to 
the  other  in  all  directions,  as  shown  in  Fig.  44,  p.  149.  Every  celes- 
tial meridian  coincides  with  the  terrestrial  meridian  of  some  point  on 
the  earth. 

Metonic  Cycle.     See  p.  48. 

Micrometer  {small  measurer).  Any  instrument  for  the  accurate  measure- 
ment of  very  small  distances  or  angles. 

Nadir.  The  point  of  the  celestial  sphere  directly  beneath  our  feet,  or  the 
direction  exactly  downwards. 

Node.  The  point  in  which  an  orbit  intersects  the  ecliptic,  or  other  plane 
of  reference.     See  Elements,  and  p.  23. 

Nutation.  A  very  small  oscillation  of  the  direction  of  the  earth's  axis. 
It  arises  from  the  fact  that  the  forces  which  produce  the  precession  of 
the  equinoxes  do  not  act  uniformly,  and  may  therefore  be  considered  as 
the  inequality  of  precession  arising  from  the  inequality  of  the  force 
which  produces  it. 

Oblate.  Applied  to  a  round  body  which  differs  from  a  sphere  in  being 
flattened  at  the  poles,  as  in  the  case  of  the  earth. 

Obliquity  of  the  Ecliptic.  The  inclination  of  the  plane  of  the  equator 
to  that  of  the  ecliptic,  which  is  equal  to  half  the  difference  between  the 
greatest  meridian  altitude  of  the  sun,  which  occurs  about  June  21st,  and 
the  least,  which  occurs  about  December  21st.  At  the  beginning  of  1850 
its  value  was  about  23°  27^',  and  it  is  diminishing  at  the  rate  of  about 
47"  per  century. 

Occultation  (a  hiding).  The  disappearance  of  a  distant  body  through  the 
interposition  of  a  nearer  one  of  greater  angular  magnitude.  Applied 
especially  to  the  case  of  the  moon  passing  over  a  star  or  planet,  and  to 
that  of  Jupiter  hiding  one  of  his  satellites. 

Opposition.  The  relation  of  two  bodies  in  opposite  directions.  The 
planets  are  said  to  be  in  opposition  when  their  longitude  differs  180° 
from  that  of  the  sun,  so  that  they  rise  at  sunset,  and  set  at  sunrise. 

Orbit.  The  patli  described  by  a  planet  around  the  sun,  or  by  a  satellite 
around  its  primary  planet. 

Parallax.     The  difference  of  direction  of  a  hei^venly  body  as  seen  from 


GLOSSARY  OF  TECHNICAL  TERMS.  669 

two  points,  as  tho  centre  of  the  earth  and  some  point  on  its  snrface. 

See  Part  II.,  Chap.  III.,  $  1. 
Parallels.     Iniagiuary  circles  on  the  earth  or  in  tho  heavens  parallel  to 

the  equator,  and  having  the  pole  as  their  centre.    The  parallel  of  40°  N. 

is  one  which  is  everywhere  40°  from  the  equator  and  50°  from  the  north 

pole.     See  Fig.  44,  p.  149. 
Penumbra.     A  partial  shadowing.     Applied  generally  in  cases  where 

light  is  partially,  hut  not  entirely,  cut  off. 
Peri-  {near).     A  general  prefix  to  denote  the  point  at  which  a  hody  revolv- 
ing in  orbit  comes  nearest  its  centre  of  motion ;  as,  perihelion,  the  point 

nearest  the  sun;  ]}eri(jee,  that  nearest  the  earth;  peri- Saturnium,  that 

nearest  the  planet  Saturn, etc. 
Perturbation.     A  disturbance  in  the  regular  elliptic  or  other  motion  of  a 

heavenly  body,  pi'oduced  by  some  force  additional  to  that  which  causes 

its  regular  motion.     The  perturbations  of  the  planets  are  caused  by 

their  attraction  on  each  other. 
Photometer  {light-measurer).     An  instrument  for  estimating  the  intensity 

of  light.     The  number  of  kinds  of  photometers  is  very  great. 
Precession  of  the  Equinoxes.      A  motion  of  the  pole  of  the  equator 

around  that  of  the  ecliptic  in  about  26,000  years.     See  pp.  19, 62, 88. 
Prime  Vertical.     The  vertical  circle  passing  due  east  and  west  through 

the  zenith,  and  therefore  intersecting  the  horizon  in  its  east  and  west 

points. 
Quadrature.     The  positions  of  the  moon  when  she  is  90°  from  the  sun, 

and  therefore  in  her  first  or  last  quarter. 
Radiant  Point.     That  point  of  the  heaA'cns  from  which  the  meteors  all 

seem  to  diverge  during  a  meteoric  shower.    See  p.  390. 
Refraction  (a  Ireaking).    The  bending  of  a  ray  of  light  by  passing  through 

a  medium.    Astronomical  refraction  means  the  refraction  of  the  light  of  a 

heavenly  body  caused  by  the  atmosphere,  as  described  on  p.  300. 
Retrograde  (hackward).     Applied  to  the  motion  of  a  planet  from  east  to 

west  among  the  stars. 
Saros.     A  period  or  cycle  of  18  years  11  days,  in  which  eclipses  recur. 

See  p.  30. 
Scintillation  (a  tivinkling).     The  twinkling  of  the  stars. 
Secular  (relating  to  the  ages).     Applied  to  those  changes  in  tho  planetary 

orbits  which  require  immense  periods  for  their  completion.     See  p.  95. 
Selenography.     A  description  of  the  surface  of  the  moon,  as  geography  is 

a  description  of  the  earth's  surface.     We  might  call  it  lunar  geography 

but  for  the  etymological  absurdity. 
Sexagesimal.     Counting  by  sixties.     Applied  to  those  denominate  sys- 
tems in  which  one  unit  is  sixty  times  the  next  inferior  one,  as  the  usual 

subdivision  of  time  and  arc. 


570  APPENDIX. 

Seztant  Tbc  sixth  part  of  a  circumference.  Also  an  instrnment  much 
nsediu  practical  astronomy  and  navigation, for  the  ready  nieasnrement  of 
the  angular  distance  of  two  points,  or  of  the  altitude  of  a  heavenly  body. 

Sidereal  Relating  to  the  stars.  Sidereal  time  is  time  measured  by  the 
diurnal  revolution  of  the  stars.  Each  unit  of  sidereal  time  is  about 
^^th  part  shorter  than  the  usual  one.     See  p.  152. 

Signs  of  the  Zodiac.  The  twelve  equal  parts  into  which  the  ecliptic  or 
zodiac  was  divided  by  the  ancient  astronomers.  These  signs,  begin- 
ning at  the  vernal  equinox,  are : 


Aries,  the  Ram. 
Tauniit,  the  Bull. 
Gemini,  the  Twins. 
Cancer,  the  Crab. 
Leo,  the  Lion. 
Virao.  the  Virgin. 


Libra,  the  Balance. 
Scorpins,  the  Scorpion. 
Sagittarius,  the  Archer. 
Capncomtis,  the  Goat. 
Aquarius,  the  Water-bearer. 
Pisces,  the  Fishes. 


Solstices  (sianding-poinis  of  the  sun).  Those  points  of  the  ecliptic  which 
are  most  distant  from  the  equator,  and  through  which  the  sun  passes 
about  June  2l3t  and  December  21st.  So  called  because  the  suu,  having 
then  attained  its  greatest  declination,  stops  its  motion  in  declination, 
and  begins  to  return  towards  the  equator.  The  two  solstices  are  desig- 
nated as  those  of  summer  and  winter  respectively,  the  first  being  in  6 
hours  and  the  second  iu  IS  hours  of  right  ascension. 

Sothic  Period.  That  iu  which  the  Egyptian  year  of  365  days  correspond- 
ed in  succession  to  all  the  seasons.  The  equinoctial  year  being  supposed 
to  be  365J  days,  this  period  would  be  1461  years,  but  it  is  really  longer. 
See  p.  47. 

Spectilum  (a  mirror).    The  concave  mirror  of  a  reilecting  telescope. 

Stationary.  Applied  to  those  asjjects  of  the  planets  occurring  between 
the  periods  of  direct  and  retrograde  motion  when  they  appear  for  a  short 
time  not  to  move  relatively  to  the  stars. 

S3rnodic.  Applied  to  movements  or  periods  relative  to  the  sun.  The 
synodic  movement  of  a  planet  is  the  amount  by  which  its  motion  ex- 
ceeds or  falls  short  of  that  of  the  earth  round  the  sun,  while  its  synodic 
period  is  the  time  which  elapses  between  two  consecutive  returns  to 
inferior  or  superior  conjunction,  or  to  opposition. 

Syzygy.  The  points  of  the  moon's  orbit  in  which  it  is  either  new  moon  or 
full  moon.  The  line  of  the  syzygies  is  that  which  passes  through  these 
points,  crossing  the  orbit  of  the  moon. 

Terminator.  The  bounding  line  between  light  and  darkness  on  the  moon 
or  a  planet. 

Transit  (a  passing  across).  The  passage  of  an  object  across  some  fixed  line, 
as  the  meridian,  for  example,  or  between  the  eye  of  an  observer  and  an 
apparently  larger  object  beyond,  so  that  the  nearer  object  appears  on 
the  face  of  the  more  distant  one.    Applied  especially  to  passages  of  Mer- 


GLOSSARY  OF  TECHNICAL   TERMS.  571 

cury  and  Venus  over  the  disk  of  the  son,  and  of  the  satellites  of  Jupiter 
over  the  disk  of  the  planet. 

iTrepidation.  A  slow  oscillation  of  the  ecliptic,  having  a  period  of  7000 
years,  imagined  by  the  Arabian  astronomers  to  account  for  the  discord- 
ance in  the  determinations  of  the  precession  of  the  equinoxes.  In  con- 
sequence of  this  motion  the  equinox  was  supposed  to  oscillate  backward 
and  forward  through  a  space  of  about  twenty  degrees.  The  trepidation 
continued  to  figure  in  astronomical  tables  until  the  end  of  the  sixteenth 
century,  but  it  is  now  known  to  have  no  foundation  in  fact. 

Umbra  (a  shadoiv).  That  darkest  part  of  the  shadow  of  an  object  where 
no  part  of  the  luminous  object  can  be  seen.  Also,  the  interior  and  dark- 
est part  of  a  sun-spot. 

Vertical,  Angle  of.  The  small  angle  by  which  the  real  direction  of  the 
earth's  centre  from  any  point  on  its  surface  differs  from  that  which  is 
directly  downward,  as  indicated  by  the  i)lumb-line.  It  arises  from  the 
elipticity  of  the  earth,  vanishes  at  the  equator  and  poles,  and  attains  its 
greatest  value  of  about  12'  at  the  latitude  of  45°. 

Vortex  (rt  whirlpool) ;  pi.  Vortices.  The  theory  of  vortices  is  that  which 
assumed  the  heavenly  bodies  to  be  carried  round  in  a  whirling  fluid. 
See  p.  72. 

Zenith.  The  poiut  of  the  celestial  sphere  which  is  directly  overhead,  and 
from  which  a  phinib-liue  falls.  The  geocentric  zenith  is  the  poiut  in  which 
a  straight  line  rising  from  the  centre  of  the  earth  intersects  the  celestial 
sphere.  It  is  a  little  nearer  the  celestial  equator  than  the  apparent  or 
astronomical  zenith,  owing  to  the  ellipticity  of  the  earth.  Sec  Vertical, 
Angle  of. 

Zodiac.  A  belt  encircling  the  heavens  on  each  side  of  the  ecliptic,  within 
which  the  larger  planets  always  remain.  Its  breadth  is  generally  con- 
sidered to  be  about  sixteen  degrees — eight  degrees  on  each  side  the 
ecliptic.  In  the  older  astronomy  it  was  divided  up  into  twelve  parts, 
called  signs  of  the  zodiac. 


INDEX. 


PAGE 

Abbe,  distribution  of  the  nebnlse 464 

parallax  of  Sirius 549 

Aberration  of  light  described 209 

Acceleration  of  moon's  motion 9G 

Adams  determines  moon's  acceleration.    90 

investigates  motions  of  Uranus 3GS 

Aerolites,  description  i  T 399,  401 

Airy,  his  water  telescope 212 

density  of  the  earth 46 

A  Igol  a  variable  star 43S 

Apparition,  circle  of  perpetual 11 

Argelander  catalogues  the  stars 42C 

Argus,  tj,  a  variable  star 440 

Aristarchus  attempts  to  measure  the  dis- 
tance of  the  sun 22 

Aeten,  motion  of  Eucke's  comet 394 

Asteroids  (see  also  Planets,  small) . .  329,  542 

Astrolabe  described 107,  55S 

Astronomer  Royal,  duties  of 162 

Attraction  of  a  mountain S5 

of  small  masses 81 

Aurora,  description  of. 309 

height,  nature,  etc 310 

periodicity  of 255 

spectrum  of. Sll 

Auwers,  motion  of  Sirius  and  Procyon. .  451 

Baily  determines  density  of  earth 84 

Baily's  beads  explained 314 

Barker,  si)ectrum  of  Aurora 311 

Bayer  system  of  naming  stars 427 

Bernoulli  (J.)  sustains  theory  of  vortices.    80 

Bessel,  parallax  of  01  Cj'gni 208 

Black  drop  in  transits  of  Venus 181 

its  cause 183 

Blanchini,  his  great  telescope 114 

rotation  of  Venus 297 

Bode's  lav?  of  planetary  distances 237 

Bond  discovers  satellite  of  Saturn 358 

intensity  of  moonlight 323 

investigates  rings  of  Saturn 358 

Books,  list  of,  for  reference 555 


PAAB 

Bradley  attacks  stellar  parallax 206 

detects  aberration  of  light 209 

Brake  (Tycho),  his  obs.  and  system 66 

Brunnow,  researches  in  stellar  parallax.  210 

Calendar,  history,  etc 44 

Julian  and  Gregorian 49 

Cassegrainian  telescope 126 

Cassini  discovers  satellites  of  Saturn  . . .  360 

theory  of  Saturn's  rings 358 

Cavendish,  density  of  the  earth 82 

Cayley  determines  moon's  acceleration.    98 

Challis  searches  for  Neptune 368 

Chromosphere  of  the  sun 262 

its  violent  movements,  etc 268 

Chronograph  described 157 

Circles  of  the  celestial  sphere 143 

Clark  (Alvan),  his  telescopes 139 

discovers  companion  of  Sirius 140 

Clusters  of  stars 453 

Comet,  great,  of  1680 382 

of  1682  (Halley's) 383 

ofl843 387 

its  near  approach  to  sun. .  266 

of  1858  (Donati's) 38T 

views  of 376,  388 

of  Biela 386,  40T 

of  Encke 389 

Comets,  aspects  of,  etc .'  373 

development 374 

relations  to  meteors 403 

motions 377 

number 381 

orbits  of,  their  form 377 

physical  constitution  of. 409 

remarkable,  description  of. 382 

tails  of,  repelled  by  the  sun  . .  409 

Constellations,  antiquity  of  names 426 

description  of. 429 

Copernicus  founds  modern  astronomy. .    51 

publishes  his  system 63 

bis  system  explained 54 


574 


INDEX. 


PlOB 

Copirnieua  rep.  eccentricity  of  orbits. ...    CO 

his  distances  of  the  planets 60 

estimate  of  his  work CI 

work  condemned  by  luquisitiou  —     72 
Cornu  measures  velocity  of  light —  216,  218 

Cormia  of  the  sun  described 258 

its  probable  nature 264 

its  spectrum 203 

Cosmogony,  the  system  of 503 

Cycle,  the  Metouic 48 

Dean  determ.  transatlantic  longitude... .  161 
Delaunay,  secular  acceleration  of  moon.    97 

Density  of  the  earth 84 

Descarten'  theory  of  vortices 72 

DonaWs  comet,  description  of 387 

views  of. 376,  388 

Draper,  his  great  telescope 137 

photograph  of  the  moon 319 

theory  of  the  solar  spectrum 228 

Earth,  density  of. 84 

elements  of  orbit 510 

figure  of,  view  of  Ptolemy 32 

on  Newton's  theory 86 

the  French  investigations.  87 

theory  of  its  fluidity 305 

difBculties  of  this  theory 306 

temperature  of  interior 304,  523 

secular  cooling  of. 523 

Easter,  how  determined 4S 

Eastman,  view  of  total  eclipse  in  1869  . .  259 

Eccentric  in  ancient  astronomy 41 

Eclipses,  geometrical  explanation 24 

classification 25 

duration  of. 28 

ancient  observations  of. 257 

seasons  and  periodic  recurrence 29 

total,  phenomena  of 258 

of  1809,  general  view  of 259 

observations  of 263 

Ecliptic,  description  of 15 

obliquity  explained 61 

Elements  of  the  planetai-y  orbits 540,  565 

Encke  determines  solar  parallax 183 

investigates  resisting  medium 387 

Epicych'.%  ancient  system  of 37 

explained  by  Copernicus 54 

Equator,  celestial 12,  149 

Evection  discovered  by  Ptolemy 43 

Eye-piece  of  telescope 120 

Faculce  of  the  sun 566 

Faye,  constitution  of  the  snn 279 

his  comet,  motions  of 391 

Fizeau  measures  velocity  of  light 215 

FoucaM?<  measures  velocity  of  light 216 


Galaxy,  or  Milky  Way,  its  aspect 428 

Galileo  reinvents  the  telescope 108 

discovers  phases  of  Venus 296 

satellites  of  Jupiter 344 

resolves  the  Milky  Way 420 

Galle,  parallax  of  asteroids 202 

optical  discoverer  of  Neptune 369 

Gentil,  his  unfortunate  voyage 182 

Gilliss,  expedition  to  Chili 176 

Glacial  epoch,  its  possible  cause 243 

Glaseriapp,  velocity  of  light 212 

Gnomon,  its  use  by  the  ancients 103 

Golden  number 48 

Gould  determ.  transatlantic  longitude  . .  161 

Gravitation  not  newly  discovered 48 

how  generalized  by  Newton 76 

universal  law  of 81 

exerted  by  small  masses 81 

explains  motion  of  the  planets  . .  .98,  102 
Grubh  constructs  Melbourne  telescope. .  134 

Hall  observes  spot  on  Saturn 349 

discovers  satellites  of  Mars 329,  331 

Halley  discovers  secular  accel.  of  moon.  96 

total  eclipse  in  1715 258 

periodicity  of  his  comet 383 

proposes  obs.  of  transit  of  Venus 178 

Hansen,  moon's  secular  acceleration 97 

solar  parallax 184 

Harkncss,  spectrum  of  the  corona 263 

observes  meteoric  shower 402 

Herschel,  his  telescopes 123 

discovery  of  Uranus 362 

of  two  satellites  of  Uranns 363 

his  star  gauges 478 

structure  of  the  universe 480 

nebular  hypothesis 507 

Song  of  the  Telescope 129 

Hilgard  determ.  transatlantic  longitude.  161 

Hipparchus  observes  motions  of  planets  40 

catalogues  the  stars 425 

JToWc/i  investigates  satellites  of  Uranus.  365 

Hooke,  problem  of  stellar  parallax 201 

Horrox  first  observes  transit  of  Venus  . .  177 

Hugging,  appearance  of  sun's  surface  . . .  239 

motion  of  stars  in  line  of  sight 468 

spectrum  of  nebulie 459 

of  new  star 447 

Huyghens  prep,  the  way  for  gravitation.  T3 

discovers  rings  of  Saturn 350 

Inquisition  condemns  work  of  Coper- 
nicus      78 

Tntra-Mercurial  planets,  supposed.  ..102,  28T 
pretended  observations  of 293 

Jansen,  supposed  inventor  of  telescope..  109 


INDEX. 


575 


Janasen  analyzes  solar  protuberauces. 

photographs  of  the  sun 

Jupiter,  the  planet 

appearance  of  surface 

elements  of  orbit 

light  and  activity  of 

rotation  of,  on  axis 

satellites  of 


PAGE 

.  200 
.  240 

.  3;i9 

.  340 
.  540 
.  342 
.  343 
.  344 

.  474 

,   505 


Kant,  structure  of  the  universe  . . . 
founds  nebular  hypothesis 

Kepler  investigates  motions  of  planets.  *JS 

first  two  laws  of  planetary  motion..  (j9 

third  law TO 

structure  of  the  universe 473 

Lambert,  structure  of  the  universe 477 

Langley,  appearance  of  the  suu 23S 

heat  of  the  sun 243,  244 

on  the  sun's  constitution 250 

Laplace,  cause  of  moon's  acceleration. . .    06 

nebular  hypothesis 507 

Lassell,  his  great  telescopes 133 

discovery  of  satellites 304,  372 

Latitude,  how  determ.  astronomically. . .  150 
Leverrier  investigates  motion  of  Mercury  102 

discovery  of  Neptune 367 

Libration  of  the  moon 313 

Light,  motion  of 208 

time  of  coming  from  sun 211 

velocity  of,  measured 213 

Lipperhey  an  inventor  of  the  telescope  .  100 
Lockyer  analyzes  sun's  protuberances. . .  261 
Longitude,  terrestrial,  how  found 152 

the  transatlantic ICl 

Loomis,  periodicity  of  the  aurora,  etc.. . .  255 

Lovcring,  periodicity  of  the  aurora 2.55 

Lyman  investigates  atmosphere  of  Venus  300 


Mars,  the  planet 

aspect  of. 

elements  of  orbit 

maps  of 328, 

rotation  of. 

satellites  of. 

Maskelyne,  attraction  of  mountain 

Maxwell,  theory  of  Saturn's  rings 

Mercury,  the  planet 

elements  of  orbit 

ancient  theory  of 

aspect  and  rotation 

motion  of  perihelion 102, 

transits  of 

Meridian  circle  described 

Meteoric  showers 

radiant  point  of 

produced  by  comet . . . 


320 
327 
640 
320 
328 
541 

85 
358 
289 
540 

40 
290 
292 
291 
154 
393 
403 
409 
38 


Meteors  ana  shooting-stars 397 

how  caused 400 

combustion  of,  by  motion 401 

orbits  of 407 

relations  to  oomets 404 

Metonic  cycle 48 

Milky  Way  described 428 

Molkr,  motion  of  Faye's  comet 395 

Month,  origin  of 45-47 

Moon,  revolution  and  phases 21 

acceleration  of  its  motion 9G 

unexplained  changes  of  motion 98 

path  among  the  stars 23 

nodes,  motion  of. 23 

eclipses  of,  how  caused 24 

gravitation  of,  found  by  Newton 76 

investigations  of  the  ancients 42 

atmosphere 320 

surface  described 317 

distance  and  magnitude 312 

figure,  rotation,  and  libratiou 313 

changes  of  surface 322 

light  and  heat  of. 323 

efi"ect  on  the  earth 325 

Music  of  the  spheres 4 

Xasmyth,  appearance  of  the  snn 23S 

Nehulw,  appearance  of 452 

views  of. 4C0,  4G2 

distribution 402 

great,  of  Orion 457 

gaseous  nature  of. 45'.i 

Nebular  hypothesis 505 

reached  by  reasoning  back- 
ward from  the  present. . .  511 

conclusions  respecting 520 

Xeptune,  history  of  its  discovery 300 

elements  of  orbit 540 

physical  aspect  of. 372 

satellite  of 372 

Xeu'all,  his  great  telescope 140 

Newton  (H.  A.),  meteoric  showers 404 

Newton  (Sir  I.),  his  work 74 

laws  of  motion 75 

theory  of  comets 415 


Olbers,  hypothesis  of  the  explosion  of  a 

planet 332,  334 

Orbits  of  the  planets 540,  542 

Parallax,  definition  of 107 

annual 172 

solar,  measures  of 1 73 

from  transit  of  Venus 177 

most  probable  value 198 

list  of  papers  on 551 

stellar,  efforts  to  find 'iOO 


576 


INDEX. 


Parallax,  list  of  measures 547  ) 

Peirce,  liugs  of  Satnrn 3^S  j 

perturbations  of  Neptnne 371  ; 

theory  of  comets 414  | 

Photosphere,  its  appearaoce 238  i 

light  and  probable  nature 269 

Pickerinrf,  intensity  of  SQulight 841 

Planets,  the  seven,  of  the  ancients 14 

order  of  distance,  ancient 40 

modern 231,  235 

laws  of  their  motion C9,  93 

secular  variations  of  orbits 95 

aspects  of. 235 

distances  and  masses 233 

of  other  suns 528 

supposed  intra-Mercnrial 102 

small,  fill  gap  between  Mars  and  Ju- 
piter   331 

earlier  discoveries 332 

number  and  mass 336 

elements  of  orbits 542 

Pleiades,  map  of. 454 

Plnrality  of  worlds 52S 

Pole  of  the  heavens 10 

Precession  of  the  equinoxes 19 

explained  by  Copernicus 62 

cause  of SS 

Proctor,  arrangement  of  the  stars 4SS 

Prominences.    See  Protuberances. 

Protuberances  of  the  sun 258 

spectroscopic  observation  of 200 

Ptolemy,  his  system  of  the  world.. . , 32j 

bis  answers  to  objectors 35 

his  relations  to  Copei-nicns 5S 

his  catalogue  of  stars 425 

Pythagoras,  crystalline  spheres  of 3 

his  supposed  system 4,  52 

Radiant  point  of  meteors 401 

Refraction,  astronomical 300 

Reich,  density  of  earth S4 

Resisting  medium,  indications  of 393 

researches  relating  to 394 

Ring«  of  Saturn 349 

Rittenhouse  observes  transit  of  Venus  . .  200 

Roemer  searches  for  stellar  parallax 201 

Rouse,  his  great  telescope 133 

heat  of  the  moon 324 

Rutherford,  photographic  measurements  ISC 

Saroa,  or  period  of  eclipses 30 

HatelliteH  of  Jupiter 344 

of  Saturn 359 

of  Uranus 363 

ofXeptune 372 

Saturn,  the  planet 346 

aspect  of 347 


PACt 

Saturn,  elements  of  orbit 540 

rotation  on  axis 34s 

remarkable  spot  on 349 

rings 349,  353 

old  views  of 351 

phasesof 352 

satellites  of 355 

Schiaparelli  theory  of  meteors 404 

Selwvfeld  catalogue  of  variable  stars  . . .  441 

Schwabe,  periodicity  of  suu-spots 264 

Seasons,  explanation  of C3 

Secchi,  temperature  of  the  snu 243 

on  the  sun's  constitution 271 

view  of  lunar  crater 321 

spectrum  of  nebula 459 

Secondary  spectrum  in  telescope 230 

Seidel,  photometric  researches 425 

Siriiis,  brilliancy  of 425 

companion  of. 451 

Solar  system,  relation  to  the  stars 103 

structure  of, 231 

plan  of 236 

Spectroscope  described 221 

Spectrum  analysis  explained 225 

Sphere,  celestial,  described 7 

circles  of 143 

Spheres,  crystalline,  of  Pythagoras 3 

Stars  (see  also  Universe) 419 

arrangement  of,  in  space 472,  490 

binary  systems  of. 450 

catalogues  of 425 

changes  among  them 471 

clusters  of 453 

constellations,  formation  of. 420 

description  of. 429 

double 448 

light  of,  how  graded 423 

magnitudes  of,  apparent 422 

intrinsic 495 

number  of,  visible 422 

motions  of,  apparent 404,  496 

in  line  of  sight 46S 

names  of,  how  given 427 

nearest 209 

new,  explanation  of 442 

nature  of 445 

observations  of  some 444 

parallaxes  of 204,  548 

probable  orbits  of  some 4,SS 

systems  of 4SS 

shooting.    See  Meteors. 

variable 438 

Stone  corrects  solar  parallax 201 

Struve  (O.),  changes  in  rings  of  Saturn. .  355 

inner  satellites  of  Uranus 364 

Struve  (W.)  investigates  stellar  parallax.  203 
parallax  of  a  Lyrse 205 


INDEX. 


577 


Strutn'  V  W  ),  structure  of  the  Universe. . .  4SG 

Sun,  age  e-if 521 

appfcrtrnDCe  of 237 

atmospppre  of 242 

coHStitiuV.n  of 204 

brightnesi?  cf,  as  a  star 491 

coutractiofl  of,  probable 519 

distance  of,  most  probable  value  of.  19S 

distauce  ot,  niettiods  of  finding 192 

gaseous  theory  of. 270 

heat  of,  quantity  radiated 243 

how  maintained 263,  517 

law  of  radiation 513  j 

motion,  apparent  annual 14 

probable  real 40U 

parallax,  how  measured 173-1!19 

most  probable  value 199 

list  of  papers  on 651 

rotation  on  axis,  law  of 255 

epots,  their  appearance 24S 

their  periodicity 254 

appear  as  cavities 251 

eurroaudings  of. 267 

temperature 243 

Telescope,  origin  of lOS 

Galilean  form  of 110 

principle  of  construction  of 110 

maguifying  power  of 112, 141 

aberration,  defect  of 112 

achromatic llC 

how  mounted  for  use 120 

reflecting,  how  made 123 

great  ones  of  modern  times 127 

list  of  the  principal 533 

rnomsoii,  rigidity  of  the  earth 304 

Tides,  how  produced 90 

friction  of,  retards  earth 98 

Time,  mean  and  apparent. 164 

Bidcreal 152 

See  also  Calendar. 

r^^MS,  law  of  planetary  distances 209 

Tranaita  of  stars,  how  observed 156 

of  Venus,  law  of  recurrence 177 

old  observations 180 

in  1S74 185,  192 

in  1882 191 


FAGK 

Tranaita  of  Mercury. 291 

Tycho  Brake,  his  work CO 

ITltigh  Beigh,  catalogue  of  stars 425 

Universe,  structure  of. 472 

stability  of,  not  necessary 602 

Uranus,  the  planet 361 

elements  of  orbit 540 

old  observations  of 363 

satellite  of. 3C3 

deviations  of  its  motion 3CC 

Venus,  ancient  theory  of  motion 39 

elements  of  orbit 540 

general  description 295 

phases 5i90 

results  of  late  transit 177 

transits  ot 177 

supposed  axial  rotation 297 

atmosphere 299 

spectrum 301 

visibility  of  dark  side 302 

satellite  of,  suspected 302 

Vojel,  photogr.  measures  of  sun's  raye.  241 

rotation  of  Venus 299 

spectrum  of  aurora 311 

views  of  Encke's  comet 375 

Vortices,  theory  of, 72 

Walker,  motions  of  Neptune 870 

Week,  days  of  the 46 

■Wlteatsto)ic  revolving  mirror 210 

Wcl/,  periodicity  of  sun-spots 254 

Wright,  spectrum  of  zodiacal  light 416 

Year,  sidereal  and  tropical 20 

young,  constitution  of  the  sun 282 

researches  in  spectrum  analysis 263 

Zodiac,  definition  of 15 

signs  of 16 

Zodiacal  light 295,  410 

Zollner,  law  of  sun's  rotation 256 

nature  of  photosphere 270 

intensity  of  moonlight 323 

theory  of  comets 415 


EXPLANATION  OF  THE  STAR  MAPS. 

These  maps  show  all  the  stars  to  the  fifth  magnitnde  inclusive  be- 
tween the  north  pole  and  40^  south  declination,  the  middle  of  each  map 
extending  to  50'  declination.  They  therefore  include  all  the  stars  which 
can  be  readily  seen  with  the  naked  eye  in  our  latitudes,  except  the  very 
smallest.  They  are,  for  the  most  part,  founded  on  Heis's  Atlas  Ccelestit 
and  the  catalogue  accompanying  it. 

To  recognize  the  constellations  on  the  maps,  reference  may  be  had  to 
the  descriptions  on  pp.  41S-4-26-  To  find  what  constellations  are  on  the 
meridian  at  any  hour  of  any  day  in  the  year,  it  will  be  necessary  to  cal™ 
cnlate  the  sidereal  time  by  the  precepts  on  p.  1.51 :  the  corresponding  hour 
of  right  ascension  is  then  to  be  sought  arouud  the  margin  of  Map  I.,  and 
at  the  top  and  bottom  of  the  other  maps.  Then,  if  Map  I.  be  held  with 
this  hour  upwards,  it  will  show  the  exact  position  of  the  northern  constel- 
lations, while  on  Maps  II.-V.  it  will  show  the  position  of  the  meridian. 
Each  of  these  four  last  maps  extends  about  from  the  zenith  to  the  south 
horizon. 

The  several  dates  on  the  ecliptic  show  the  positions  of  the  sun  during 
its  apparent  annual  course  as  described  iu  part  i.,  chap,  i.,  6  3,  and  ex- 
l)lained  on  j)p.  54,  55.  The  apparent  path  of  the  moon  iu  1877  is  marked 
out,  in  order  to  illustrate  0  6,  p.  21. 

To  illustrate  precession,  the  position  of  the  equator  2000  years  ago  is 
shown  on  Map  II.,  where  it  can  be  compared  with  the  present  position, 
marked  0''  on  the  sides  of  Maps  II.-Y.  For  the  same  object  the  circle 
which  the  celestial  pole  seems  to  describe  around  the  pole  of  the  ecliptic 
iu  25,000  years  is  shown  on  Map  I. 

The  small  circles  marked  here  and  there  on  the  maps  show  the  positions 
of  the  more  remarkable  nebulae  and  star  clusters,  a  list  of  which  is  give.; 
lu  No.  III.  of  the  Api>cti(lix. 


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